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

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The term "universally measurable" may be applied to
 
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* a [[measurable space]];
 
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* a subset of a measurable space;
 
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* a [[metric space]].
 
  
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Let $(X,\A)$ be a measurable space. A subset $A\subset X$ is called universally measurable, if it is $\mu$-measurable for every finite measure $\mu$ on $(X,\A)$. In other words: $\mu_*(A)=\mu^*(A)$ where $\mu_*,\mu^*$ are the inner and outer measures for $\mu$, that is,
 
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: $ \mu_*(A) = \max\{\mu(B):B\in\A,B\subset A\}\,,\quad
 
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\mu^*(A) = \min\{\mu(B):B\in\A,B\supset A\}\,.$
 

Revision as of 19:34, 16 February 2012

How to Cite This Entry:
Boris Tsirelson/sandbox1. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Boris_Tsirelson/sandbox1&oldid=21101
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