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Difference between revisions of "User:Boris Tsirelson/sandbox1"

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''Also: analytic measurable space''
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<ref> [http://hea-www.harvard.edu/AstroStat http://hea-www.harvard.edu/AstroStat]; <nowiki> http://www.incagroup.org </nowiki>; <nowiki> http://astrostatistics.psu.edu </nowiki> </ref>
  
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[[:Category:Classical measure theory]]
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====Notes====
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<references />
  
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{{User:Rehmann/sandbox/MSC|28A05|03E15,54H05}}
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-------------------------------------------
  
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$ \newcommand{\R}{\mathbb R}
 
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\newcommand{\C}{\mathbb C}
 
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\newcommand{\Om}{\Omega}
 
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\newcommand{\A}{\mathcal A}
 
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\newcommand{\B}{\mathcal B}
 
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\newcommand{\P}{\mathbf P} $
 
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A [[measurable space|Borel space]] $(X,\A)$ is called '''analytic''' if it is countably separated and isomorphic to a quotient space of a standard Borel space.
 
  
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====References====
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{|
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<table><TR><TD  valign="top">[1]</TD> <TD valign="top">Alexander S.  Kechris, "Classical descriptive set theory", Springer-Verlag (1995) | {{MR|1321597}} | {{ZBL|0819.04002}}</TD></TR>
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| A || B || C
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<TR><TD  valign="top">[2]</TD> <TD valign="top">Richard M.  Dudley, "Real analysis and probability", Wadsworth&Brooks/Cole  (1989) | {{MR|0982264}} | {{ZBL|0686.60001}}</TD></TR>
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|-
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<TR><TD  valign="top">[3]</TD><TD valign="top">George W. Mackey, "Borel structure in groups and their duals", ''Trans. Amer. Math. Soc.''  '''85''' (1957), 134–165 | {{MR|0089999}} |  {{ZBL|0082.11201}}</TD></TR>
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| X || Y || Z
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</table>
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|}
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-----------------------------------------
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-----------------------------------------
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$\newcommand*{\longhookrightarrow}{\lhook\joinrel\relbar\joinrel\rightarrow}$
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<asy>
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size(100,100);
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label(scale(1.7)*'$T(\\Sigma)\hookrightarrow T(\\Sigma,X)$',(0,0));
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</asy>
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<asy>
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size(220,220);
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 +
import math;
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int kmax=40;
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guide g;
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for (int k=-kmax; k<=kmax; ++k) {
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  real phi = 0.2*k*pi;
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  real rho = 1;
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  if (k!=0) {
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    rho = sin(phi)/phi;
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  }
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  pair z=rho*expi(phi);
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  g=g..z;
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}
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draw (g);
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defaultpen(0.75);
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draw ( (0,0)--(1.3,0), dotted, Arrow(SimpleHead,5) );
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dot ( (1,0) );
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label ( "$a$", (1,0), NE );
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</asy>

Latest revision as of 07:12, 13 March 2016

[1]

Notes

  1. ↑ http://hea-www.harvard.edu/AstroStat; http://www.incagroup.org ; http://astrostatistics.psu.edu


A B C
X Y Z


$\newcommand*{\longhookrightarrow}{\lhook\joinrel\relbar\joinrel\rightarrow}$

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