Namespaces
Variants
Actions

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

From Encyclopedia of Mathematics
Jump to: navigation, search
(Blanked the page)
Line 1: Line 1:
−
$\newcommand{\Om}{\Omega}
 
−
\newcommand{\A}{\mathcal A}
 
−
\newcommand{\B}{\mathcal B}
 
−
\newcommand{\M}{\mathcal M} $
 
−
The term "universally measurable" may be applied to
 
−
* a [[measurable space]];
 
−
* a subset of a measurable space;
 
−
* a [[metric space]].
 
  
−
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,
 
−
: $ \mu_*(A) = \max\{\mu(B):B\in\A,B\subset A\}\,,\quad
 
−
\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=21102
Retrieved from "https://encyclopediaofmath.org/index.php?title=User:Boris_Tsirelson/sandbox1&oldid=21102"