Namespaces
Variants
Actions

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

From Encyclopedia of Mathematics
Jump to: navigation, search
Line 6: Line 6:
 
draw((-4,0)--(4,0));
 
draw((-4,0)--(4,0));
 
</asy>
 
</asy>
 +
 +
Every narrow neighborhood of a probability measure $\mu$ is also a wide neighborhood of $\mu$. Here is a proof. Given $\varepsilon$, we take a compactly supported continuous $f:X\to[0,1]$ such that $\int f \rd\mu > 1-\varepsilon$.

Revision as of 08:21, 9 August 2012

Every narrow neighborhood of a probability measure $\mu$ is also a wide neighborhood of $\mu$. Here is a proof. Given $\varepsilon$, we take a compactly supported continuous $f:X\to[0,1]$ such that $\int f \rd\mu > 1-\varepsilon$.

How to Cite This Entry:
Boris Tsirelson/sandbox1. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Boris_Tsirelson/sandbox1&oldid=27457