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* [http://www.tau.ac.il/~tsirel/ My website]
+
My [http://www.tau.ac.il/~tsirel/ homepage] at School of Mathematics, Tel Aviv University.
−
* My user pages on other wikis: [http://en.wikipedia.org/wiki/User:Tsirel Wikipedia], [http://en.citizendium.org/wiki/User:Boris_Tsirelson Citizendium], [http://knowino.org/wiki/User:Boris_Tsirelson Knowino]
+
 
 +
My [http://en.wikipedia.org/wiki/User:Tsirel user page] on Wikipedia.
 +
 
 +
My research interests are in [[:Category:Probability theory and stochastic processes|probability]].
 +
 
 +
* ''Boris has [https://en-exact-sciences.tau.ac.il/math/Tsirelsonborisen passed away] on January 21, 2020. May he rest in peace.''
  
 
==My contributions==
 
==My contributions==
  
−
[[Measurable space]]
+
[[Measurable space]] (50,000+ views);
 +
[[Standard Borel space]] (12,000+ views);
 +
[[Analytic Borel space]] (5,000+ views);
 +
[[Universally measurable]] (5,000+ views);
 +
[[Measure space]] (20,000+ views);
 +
[[Standard probability space]] (6,000+ views);
 +
[[Measure algebra (measure theory)]] (7,000+ views).
 +
 
 +
===Wanted===
 +
 
 +
[[Random matrix]]
 +
+ [[SLE]]
 +
+ [[Gaussian measure]]
 +
 
 +
And maybe:
 +
[[Borel equivalence relation]] (see [http://en.wikipedia.org/wiki/Talk:Borel_equivalence_relation WP])
 +
 
 +
===Require revision===
 +
 
 +
[[Bell inequalities]]
 +
+ [[Probability of large deviations]]
  
 
==Some statistics==
 
==Some statistics==
  
−
We have 40+ articles with 40+ views each. [http://www.encyclopediaofmath.org/index.php/Special:PopularPages?limit=11&offset=39]
+
We have 2590+ articles viewed 2590+ times each. [https://www.encyclopediaofmath.org/index.php/Special:PopularPages?limit=21&offset=2589]
 +
 
 +
History: Dec 2011: 40×40; Jan 2012: 60×60; Feb 2012: 90×90; Mar 2012: 140×140; Apr 2012: 200×200; May 2012: 250×250; Jun 2012: 320×320; Jul 2012: 370×370; Aug 2012: 410×410; Sep 2012: 460×460; Oct 2012: 520×520; Nov 2012: 590×590; Dec 2012: 650×650; Jan 2013: 710×710; Feb 2013: 760×760; Mar 2013: 820×820; Apr 2013: 890×890; May 2013: 940×940; Jun 2013: 990×990; Jul 2013: 1040×1040; Aug 2013: 1080×1080; Sep 2013: 1130×1130; Oct 2013: 1170×1170; Nov 2013: 1220×1220; Dec 2013: 1260×1260; Jan 2014: 1300×1300; Feb 2014: 1330×1330; Mar 2014: 1380×1380; Apr 2014: 1420×1420; May 2014: 1480×1480; Jun 2014: 1520×1520; Jul 2014: 1600×1600; Aug 2014: 1640×1640; Sep 2014: 1700×1700; Oct 2014: 1760×1760; Nov 2014: 1800×1800; Dec 2014: 1860×1860; Jan 2015: 1920×1920; Feb 2015: 1960×1960; Mar 2015: 2020×2020; Apr 2015: 2080×2080; May 2015: 2140×2140; June 2015: 2180×2180; Aug 2015: 2260×2260; Sep 2015: 2280×2280; Oct 2015: 2290×2290; Nov 2015: 2300×2300; Dec 2015: 2310×2310; Jan 2016: 2320×2320; Feb 2016: 2340×2340; Jun 2016: 2400×2400; Oct 2016: 2480×2480; Feb 2017: 2590x2590.
 +
 
 +
<DynamicArticleList>
 +
  title=New articles
 +
count=10
 +
categoryRoot=Mathematics
 +
</DynamicArticleList>
 +
 
 +
<DynamicArticleList>
 +
  title=Recently updated
 +
  type=update
 +
count=10
 +
categoryRoot=Mathematics
 +
</DynamicArticleList>
 +
 
 +
<DynamicArticleList>
 +
  title=Recently discussed
 +
  type=discussion
 +
count=10
 +
categoryRoot=Mathematics
 +
</DynamicArticleList>
 +
 
 +
<DynamicArticleList>
 +
  title=Most popular
 +
  type=hot
 +
  count=10
 +
categoryRoot=Mathematics
 +
</DynamicArticleList>
 +
 
 +
==Notes to myself==
 +
 
 +
Measurable space: 48149 views at 14 November 2015; 49,116 views at 1 July 2016; 52,310 views at 7 March 2017.
 +
Rigid analytic space: 2298 views at 14 November 2015; 2,454 views at 1 July 2016; 2,749 views at 7 March 2017.
 +
 
 +
===Internal links===
 +
[[Talk:EoM:This project]]
 +
+ [[Help:MSC Templates]]
 +
+ [[User:Ulf Rehmann/Predefined TeX Macros]]
 +
+ [[Help:HowTo EoM]]
 +
+ [[User talk:Ulf Rehmann]]
 +
+ [[User talk:Nbrothers]]
 +
+ [[Encyclopedia of Mathematics:Administrators]]
 +
+ [https://www.encyclopediaofmath.org/index.php?title=Special%3APrefixIndex&prefix=&namespace=12 all help pages]
  
−
==Links==
 
−
===Internal===
 
 
[[Special:PopularPages|Popular pages]]
 
[[Special:PopularPages|Popular pages]]
−
+
 
 
+ [[Special:Statistics|Statistics]]
 
+ [[Special:Statistics|Statistics]]
 
+ [[Special:Version|Version]]
 
+ [[Special:Version|Version]]
Line 21: Line 87:
 
+ [[Special:Categories|Categories]]
 
+ [[Special:Categories|Categories]]
 
+ [[Special:WantedCategories|Wanted categories]]
 
+ [[Special:WantedCategories|Wanted categories]]
−
+ [http://www.encyclopediaofmath.org/index.php?title=Special%3AAllPages&from=&to=&namespace=10 Templates]
+
+ [[:Category:Deficient]]
 +
+ [https://www.encyclopediaofmath.org/index.php?title=Special%3AAllPages&from=&to=&namespace=10 Templates]
 +
 
 +
Non-Asy:
 +
[[Hysteron]]
 +
+ [[Ellipse]]
 +
+ [[Automata, methods of specification of]]
 +
+ [[Pascal geometry]]
 +
+ [[Braided group]]
 +
+ [[Differential geometry]]
 +
+ [[Hypergraph]]
 +
+ [[Torus knot]]
 +
+ [[Equal content and equal shape, figures of]]
 +
+ [[System of subvarieties]]
 +
 
 +
Partially Asy: [[Wild knot]]
  
−
===External===
+
Asy: [[Sinusoid]]
 +
+ [[Cantor ternary function]]
 +
+ [[Caustic]]
 +
+ [[Non-precise data]]
 +
+ [[Golden ratio]]
 +
+ [[Kolmogorov test]]
 +
+ [[Power function]]
 +
+ [[Sinusoidal spiral]]
 +
 
 +
===Maybe need more attention===
 +
* [[Special:Contributions/Ginachoi002]]
 +
* [[Lindelöf hypothesis]]
 +
* [[Cullinane diamond theorem]] (refs format)
 +
* [[Genetic Algorithms]] (title capitalization; refs format)
 +
* [[Modulus in algebraic number theory]] + [[Continuant]] + [[ABC conjecture]] (refs format)
 +
* [[Lindenbaum method]] (refs format)
 +
* [[Arithmetization of analysis]] (formulas format;  refs format)
 +
 
 +
===External links===
 
[http://msc2010.org/mscwiki/index.php?title=Main_Page MSC wiki]
 
[http://msc2010.org/mscwiki/index.php?title=Main_Page MSC wiki]
 +
+ [http://www.mediawiki.org/wiki/Extension:QuestyCaptcha QuestyCaptcha]
 +
+ [http://en.wikipedia.org/wiki/Wikipedia:WikiProject_Spam WikiProject Spam]
 +
+ [http://en.wikipedia.org/wiki/User:XLinkBot WP:XLinkBot]
 +
+ [http://www.communitywiki.org/WikiSpam WikiSpam]
 +
+ [http://asymptote.sourceforge.net/ Asymptote]
 +
 +
[http://ncatlab.org/nlab/show/HomePage nLab]
 +
+ [http://texnicalstuff.blogspot.co.il/p/table-of-contents.html TeX-nical Stuff]
 +
 +
[http://ref.subwiki.org/wiki/Main_Page Subject Wikis]
 +
 +
[https://meta.wikimedia.org/wiki/Grants:IdeaLab/PlanetMath_Books_Project PlanetMath Books Project]
 +
 +
[https://fr.wikipedia.org/wiki/Utilisateur:Claudeh5?setlang=en Claude Henri Picard (Claudeh5)]
 +
 +
===Probability (and related) articles===
 +
[[Absorbing state]]
 +
+ [[Approximation by periodic transformations]]
 +
+ [[Arcsine distribution]]
 +
+ [[Asymptotic negligibility]]
 +
+ [[Attraction domain of a stable distribution]]
 +
 +
[[Baire set]]
 +
+ [[Bellman–Harris process]]
 +
+ [[Bernoulli theorem]]
 +
+ [[Bernoulli trials]]
 +
+ [[Binomial distribution]]
 +
+ [[Birkhoff ergodic theorem]]
 +
+ [[Borel measure]]
 +
+ [[Borel space]]
 +
+ [[Borel strong law of large numbers]]
 +
+ [[Borel–Cantelli lemma]]
 +
+ [[Branching process]]
 +
+ [[Branching process, age-dependent]]
 +
+ [[Branching process with a random medium]]
 +
+ [[Branching process with immigration]]
 +
+ [[Branching processes, regularity of]]
 +
+ [[Brownian motion]]
 +
 +
[[Cauchy distribution]]
 +
+ [[Central limit theorem]]
 +
+ [[Characteristic function]]
 +
+ [[Chebyshev inequality in probability theory]]
 +
+ [[Continuous distribution]]
 +
+ [[Continuous flow]]
 +
+ [[Convergence, types of]]
 +
+ [[Convergence in distribution]]
 +
+ [[Convergence in probability]]
 +
+ [[Convergence of measures]]
 +
+ [[Cramér theorem]]
 +
+ [[Cramér–von Mises test]]
 +
 +
[[Diffusion process]]
 +
+ [[Discrete distribution]]
 +
+ [[Dispersion]]
 +
+ [[Distribution function]]
 +
+ [[Distributions, convergence of]]
 +
+ [[Dynamical system]]
 +
 +
[[Edgeworth series]]
 +
+ [[Elementary flow]]
 +
+ [[Entropy theory of a dynamical system]]
 +
+ [[Ergodic theorem]]
 +
+ [[Ergodic theory]]
 +
+ [[Ergodicity]]
 +
+ [[Exponential distribution]]
 +
 +
[[Feller process]]
 +
+ [[Flow (continuous-time dynamical system)]]
 +
+ [[Functional of a Markov process]]
 +
 +
[[Galton–Watson process]]
 +
+ [[Gaussian process]]
 +
+ [[Geometric distribution]]
 +
+ [[Gram–Charlier series]]
 +
 +
[[Infinitely-divisible distribution]]
 +
 +
[[Kolmogorov equation]]
 +
+ [[Kolmogorov test]]
 +
+ [[Kolmogorov–Chapman equation]]
 +
+ [[Kolmogorov–Smirnov test]]
 +
 +
[[Laplace theorem]]
 +
+ [[Law of large numbers]]
 +
+ [[Law of the iterated logarithm]]
 +
+ [[Lebesgue integral]]
 +
+ [[Limit theorems]]
 +
+ [[Lévy canonical representation]]
 +
+ [[Lévy metric]]
 +
 +
[[Markov chain]]
 +
+ [[Markov chain, class of zero states of a]]
 +
+ [[Markov chain, decomposable]]
 +
+ [[Markov chain, generalized]]
 +
+ [[Markov chain, non-decomposable]]
 +
+ [[Markov chain, periodic]]
 +
+ [[Markov chain, recurrent]]
 +
+ [[Markov moment]]
 +
+ [[Markov process]]
 +
+ [[Markov property]]
 +
+ [[Martingale]]
 +
+ [[Mathematical expectation]]
 +
+ [[Mathematical statistics]]
 +
+ [[Maximal ergodic theorem]]
 +
+ [[Measurable flow]]
 +
+ [[Measurable function]]
 +
+ [[Measurable space]]
 +
+ [[Measure-preserving transformation]]
 +
+ [[Median (in statistics)]]
 +
+ [[Metric isomorphism]]
 +
+ [[Metric transitivity]]
 +
+ [[Mixing]]
 +
+ [[Multinomial distribution]]
 +
 +
[[Normal distribution]]
 +
+ [[Normal number]]
 +
 +
[[Operator ergodic theorem]]
 +
+ [[Ornstein–Chacon ergodic theorem]]
 +
 +
[[Poisson distribution]]
 +
+ [[Poisson process]]
 +
+ [[Poisson theorem]]
 +
+ [[Probabilistic metric space]]
 +
+ [[Probability]]
 +
+ [[Probability distribution]]
 +
+ [[Probability measure]]
 +
+ [[Probability of large deviations]]
 +
+ [[Probability space]]
 +
+ [[Probability theory]]
 +
 +
[[Quantile]]
 +
 +
[[Random variable]]
 +
 +
[[Separable process]]
 +
+ [[Sequential analysis]]
 +
+ [[Serial scheme]]
 +
+ [[Spectrum of a dynamical system]]
 +
+ [[Stable distribution]]
 +
+ [[Standard Borel space]]
 +
+ [[Stationary distribution]]
 +
+ [[Stationary stochastic process]]
 +
+ [[Statistical physics, mathematical problems in]]
 +
+ [[Stochastic differential equation]]
 +
+ [[Stochastic equivalence]]
 +
+ [[Stochastic indistinguishability]]
 +
+ [[Stochastic integral]]
 +
+ [[Stochastic matrix]]
 +
+ [[Stochastic process]]
 +
+ [[Stochastic process with independent increments]]
 +
+ [[Stochastic process with stationary increments]]
 +
+ [[Strange attractor]]
 +
+ [[Strong law of large numbers]]
 +
 +
[[Transition-operator semi-group]]
 +
+ [[Transition function]]
 +
+ [[Transition with prohibitions]]
 +
+ [[Triangular array]]
 +
 +
[[Uniform distribution]]
 +
 +
[[Variance]]
 +
+ [[Von Neumann ergodic theorem]]
 +
 +
[[Weak convergence of probability measures]]
 +
+ [[Wiener process]]
 +
---------------
 +
[[Absolute continuity]]
 +
+ [[Absolutely continuous measures]]
 +
+ [[Accessible random variable]]
 +
+ [[Additive function]]
 +
+ [[Additive noise]]
 +
+ [[Additive stochastic process]]
 +
+ [[Almost-everywhere]]
 +
+ [[A posteriori probability]]
 +
+ [[A priori probability]]
 +
+ [[Asymmetry coefficient]]
 +
+ [[Asymmetry of a distribution]]
 +
+ [[Atomic distribution]]
 +
+ [[Automaton, probabilistic]]
 +
+ [[Auto-correlation]]
 +
+ [[Autocovariance]]
 +
+ [[Auto-regression]]
 +
+ [[Auto-regressive process]]
 +
+ [[Berry-Esseen inequality]]
 +
+ [[Birth-and-death process]]
 +
+ [[Einstein-Smoluchowski equation]]
 +
+ [[Independence]]
 +
+ [[Kolmogorov inequality]]
 +
+ [[Lattice distribution]]
 +
+ [[Lebesgue integral‎]]
 +
+ [[Non-atomic measure]]
 +
+ [[Pascal distribution]]
 +
+ [[Recurrent events]]
 +
+ [[Special functions‎]]
 +
+ [[Truncated distribution]]
 +
 +
===Know-how===
 +
 +
Symbol choice: [[Talk:Variance]], [[Talk:Almost-periodic analytic function]], [[Talk:Borel-Cantelli lemma]].
 +
 +
<nowiki>#REDIRECT[[]]</nowiki>
 +
 +
<nowiki>{{Anchor|countably separated}}</nowiki>
 +
 +
<nowiki>$\int f(x)\rd x$</nowiki> &nbsp; $\int f(x)\rd x$
 +
 +
<nowiki>$\int f(x)\,\mu(\!\rd x)$</nowiki> &nbsp; $\int f(x)\,\mu(\!\rd x)$
 +
 +
<nowiki>See {{Cite|K|Sect. 12.B}}.</nowiki>
 +
 +
<nowiki>{|</nowiki><br />
 +
<nowiki>|valign="top"|{{Ref|K}}|| Alexander S.  Kechris, "Classical  descriptive set theory", Springer-Verlag (1995). &amp;nbsp;  {{MR|1321597}} &amp;nbsp; {{ZBL|0819.04002}</nowiki><br />
 +
<nowiki>|-</nowiki><br />
 +
<nowiki>|valign="top"|{{Ref|M}}||  George W.  Mackey,  "Borel structure in groups and their duals",  ''Trans.  Amer.  Math. Soc.''  '''85''' (1957), 134–165. &amp;nbsp; {{MR|0089999}} &amp;nbsp; {{ZBL|0082.11201}}</nowiki><br />
 +
<nowiki>|}</nowiki>
 +
 +
 +
====Article====
 +
''Also: standard measurable space''
 +
 +
<nowiki>{{MSC|03E15|28A05,54H05}}</nowiki>
 +
 +
<nowiki>[[Category:Descriptive set theory]]</nowiki><br>
 +
<nowiki>[[Category:Classical measure theory]]</nowiki>
 +
 +
<nowiki>$ \newcommand...$</nowiki><br>
 +
A Borel space is called '''standard''' if...
 +
 +
-----------------------------------------------------
 +
 +
<nowiki>{{MSC|60-01|60F15,60F20}}</nowiki>
 +
 +
-----------------------------------------------------
 +
 +
<nowiki>{{DEF}}</nowiki><br>
 +
This is a "wanted page". It was proposed that an entry with this title should be included.<br>
 +
<nowiki>{{TEX|want}}</nowiki><br>
 +
''subtitle''<br>
 +
<nowiki>{{MSC|...}}</nowiki><br>
 +
<nowiki>[[Category:...]]</nowiki><br>
 +
<nowiki>{{TEX|done}}</nowiki><br>
 +
 +
====Category====
 +
 +
<nowiki>* {{MSC|60J10}}</nowiki>
 +
 +
<nowiki>[[Category:Markov processes]]</nowiki>
 +
 +
--------------------------------------
 +
 +
<nowiki>* {{MSC|60Jxx}}</nowiki>
 +
 +
<nowiki>[[Category:Probability theory and stochastic processes]]</nowiki>
 +
 +
--------------------------------------
 +
 +
<nowiki>* {{MSC|60}}</nowiki>
 +
 +
<nowiki>[[Category:Probability and statistics]]</nowiki>
 +
 +
====Talk====
 +
 +
: And please sign your messages (on talk pages) with four tildas: <nowiki>~~~~</nowiki>.

Latest revision as of 05:59, 19 January 2022

My homepage at School of Mathematics, Tel Aviv University.

My user page on Wikipedia.

My research interests are in probability.

  • Boris has passed away on January 21, 2020. May he rest in peace.

My contributions

Measurable space (50,000+ views); Standard Borel space (12,000+ views); Analytic Borel space (5,000+ views); Universally measurable (5,000+ views); Measure space (20,000+ views); Standard probability space (6,000+ views); Measure algebra (measure theory) (7,000+ views).

Wanted

Random matrix + SLE + Gaussian measure

And maybe: Borel equivalence relation (see WP)

Require revision

Bell inequalities + Probability of large deviations

Some statistics

We have 2590+ articles viewed 2590+ times each. [1]

History: Dec 2011: 40×40; Jan 2012: 60×60; Feb 2012: 90×90; Mar 2012: 140×140; Apr 2012: 200×200; May 2012: 250×250; Jun 2012: 320×320; Jul 2012: 370×370; Aug 2012: 410×410; Sep 2012: 460×460; Oct 2012: 520×520; Nov 2012: 590×590; Dec 2012: 650×650; Jan 2013: 710×710; Feb 2013: 760×760; Mar 2013: 820×820; Apr 2013: 890×890; May 2013: 940×940; Jun 2013: 990×990; Jul 2013: 1040×1040; Aug 2013: 1080×1080; Sep 2013: 1130×1130; Oct 2013: 1170×1170; Nov 2013: 1220×1220; Dec 2013: 1260×1260; Jan 2014: 1300×1300; Feb 2014: 1330×1330; Mar 2014: 1380×1380; Apr 2014: 1420×1420; May 2014: 1480×1480; Jun 2014: 1520×1520; Jul 2014: 1600×1600; Aug 2014: 1640×1640; Sep 2014: 1700×1700; Oct 2014: 1760×1760; Nov 2014: 1800×1800; Dec 2014: 1860×1860; Jan 2015: 1920×1920; Feb 2015: 1960×1960; Mar 2015: 2020×2020; Apr 2015: 2080×2080; May 2015: 2140×2140; June 2015: 2180×2180; Aug 2015: 2260×2260; Sep 2015: 2280×2280; Oct 2015: 2290×2290; Nov 2015: 2300×2300; Dec 2015: 2310×2310; Jan 2016: 2320×2320; Feb 2016: 2340×2340; Jun 2016: 2400×2400; Oct 2016: 2480×2480; Feb 2017: 2590x2590.

<DynamicArticleList> 

 title=New articles
count=10
categoryRoot=Mathematics

</DynamicArticleList>

<DynamicArticleList> 

 title=Recently updated
 type=update
count=10
categoryRoot=Mathematics

</DynamicArticleList>

<DynamicArticleList> 

 title=Recently discussed
 type=discussion
count=10
categoryRoot=Mathematics

</DynamicArticleList>

<DynamicArticleList> 

 title=Most popular
 type=hot
 count=10
categoryRoot=Mathematics

</DynamicArticleList>

Notes to myself

Measurable space: 48149 views at 14 November 2015; 49,116 views at 1 July 2016; 52,310 views at 7 March 2017. Rigid analytic space: 2298 views at 14 November 2015; 2,454 views at 1 July 2016; 2,749 views at 7 March 2017.

Internal links

Talk:EoM:This project + Help:MSC Templates + User:Ulf Rehmann/Predefined TeX Macros + Help:HowTo EoM + User talk:Ulf Rehmann + User talk:Nbrothers + Encyclopedia of Mathematics:Administrators + all help pages

Popular pages + Statistics + Version

New pages + New users + Categories + Wanted categories + Category:Deficient + Templates

Non-Asy: Hysteron + Ellipse + Automata, methods of specification of + Pascal geometry + Braided group + Differential geometry + Hypergraph + Torus knot + Equal content and equal shape, figures of + System of subvarieties

Partially Asy: Wild knot

Asy: Sinusoid + Cantor ternary function + Caustic + Non-precise data + Golden ratio + Kolmogorov test + Power function + Sinusoidal spiral

Maybe need more attention

External links

MSC wiki + QuestyCaptcha + WikiProject Spam + WP:XLinkBot + WikiSpam + Asymptote

nLab + TeX-nical Stuff

Subject Wikis

PlanetMath Books Project

Claude Henri Picard (Claudeh5)

Probability (and related) articles

Absorbing state + Approximation by periodic transformations + Arcsine distribution + Asymptotic negligibility + Attraction domain of a stable distribution

Baire set + Bellman–Harris process + Bernoulli theorem + Bernoulli trials + Binomial distribution + Birkhoff ergodic theorem + Borel measure + Borel space + Borel strong law of large numbers + Borel–Cantelli lemma + Branching process + Branching process, age-dependent + Branching process with a random medium + Branching process with immigration + Branching processes, regularity of + Brownian motion

Cauchy distribution + Central limit theorem + Characteristic function + Chebyshev inequality in probability theory + Continuous distribution + Continuous flow + Convergence, types of + Convergence in distribution + Convergence in probability + Convergence of measures + Cramér theorem + Cramér–von Mises test

Diffusion process + Discrete distribution + Dispersion + Distribution function + Distributions, convergence of + Dynamical system

Edgeworth series + Elementary flow + Entropy theory of a dynamical system + Ergodic theorem + Ergodic theory + Ergodicity + Exponential distribution

Feller process + Flow (continuous-time dynamical system) + Functional of a Markov process

Galton–Watson process + Gaussian process + Geometric distribution + Gram–Charlier series

Infinitely-divisible distribution

Kolmogorov equation + Kolmogorov test + Kolmogorov–Chapman equation + Kolmogorov–Smirnov test

Laplace theorem + Law of large numbers + Law of the iterated logarithm + Lebesgue integral + Limit theorems + Lévy canonical representation + Lévy metric

Markov chain + Markov chain, class of zero states of a + Markov chain, decomposable + Markov chain, generalized + Markov chain, non-decomposable + Markov chain, periodic + Markov chain, recurrent + Markov moment + Markov process + Markov property + Martingale + Mathematical expectation + Mathematical statistics + Maximal ergodic theorem + Measurable flow + Measurable function + Measurable space + Measure-preserving transformation + Median (in statistics) + Metric isomorphism + Metric transitivity + Mixing + Multinomial distribution

Normal distribution + Normal number

Operator ergodic theorem + Ornstein–Chacon ergodic theorem

Poisson distribution + Poisson process + Poisson theorem + Probabilistic metric space + Probability + Probability distribution + Probability measure + Probability of large deviations + Probability space + Probability theory

Quantile

Random variable

Separable process + Sequential analysis + Serial scheme + Spectrum of a dynamical system + Stable distribution + Standard Borel space + Stationary distribution + Stationary stochastic process + Statistical physics, mathematical problems in + Stochastic differential equation + Stochastic equivalence + Stochastic indistinguishability + Stochastic integral + Stochastic matrix + Stochastic process + Stochastic process with independent increments + Stochastic process with stationary increments + Strange attractor + Strong law of large numbers

Transition-operator semi-group + Transition function + Transition with prohibitions + Triangular array

Uniform distribution

Variance + Von Neumann ergodic theorem

Weak convergence of probability measures + Wiener process

Absolute continuity + Absolutely continuous measures + Accessible random variable + Additive function + Additive noise + Additive stochastic process + Almost-everywhere + A posteriori probability + A priori probability + Asymmetry coefficient + Asymmetry of a distribution + Atomic distribution + Automaton, probabilistic + Auto-correlation + Autocovariance + Auto-regression + Auto-regressive process + Berry-Esseen inequality + Birth-and-death process + Einstein-Smoluchowski equation + Independence + Kolmogorov inequality + Lattice distribution + Lebesgue integral‎ + Non-atomic measure + Pascal distribution + Recurrent events + Special functions‎ + Truncated distribution

Know-how

Symbol choice: Talk:Variance, Talk:Almost-periodic analytic function, Talk:Borel-Cantelli lemma.

#REDIRECT[[]]

{{Anchor|countably separated}}

$\int f(x)\rd x$   $\int f(x)\rd x$

$\int f(x)\,\mu(\!\rd x)$   $\int f(x)\,\mu(\!\rd x)$

See {{Cite|K|Sect. 12.B}}.

{|
|valign="top"|{{Ref|K}}|| Alexander S. Kechris, "Classical descriptive set theory", Springer-Verlag (1995). &nbsp; {{MR|1321597}} &nbsp; {{ZBL|0819.04002}
|-
|valign="top"|{{Ref|M}}|| George W. Mackey, "Borel structure in groups and their duals", ''Trans. Amer. Math. Soc.'' '''85''' (1957), 134–165. &nbsp; {{MR|0089999}} &nbsp; {{ZBL|0082.11201}}
|}


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Also: standard measurable space

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A Borel space is called standard if...

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How to Cite This Entry:
Boris Tsirelson. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Boris_Tsirelson&oldid=19914
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