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

From Encyclopedia of Mathematics
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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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|valign="top"|[1]|| Alexander S.  Kechris, "Classical descriptive set theory", Springer-Verlag (1995). &nbsp; {{MR|1321597}} &nbsp;{{ZBL|0819.04002}}
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| A || B || C
 
|-
 
|-
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|valign="top"|[2]|| 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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| X || Y || Z
 
|}
 
|}
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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);
 +
label(scale(1.7)*'$T(\\Sigma)\hookrightarrow T(\\Sigma,X)$',(0,0));
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</asy>
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 +
<asy>
 +
size(220,220);
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 +
import math;
 +
 +
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);
 +
 +
defaultpen(0.75);
 +
draw ( (0,0)--(1.3,0), dotted, Arrow(SimpleHead,5) );
 +
dot ( (1,0) );
 +
label ( "$a$", (1,0), NE );
 +
 +
</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


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

How to Cite This Entry:
Boris Tsirelson/sandbox1. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Boris_Tsirelson/sandbox1&oldid=20444
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