This is an announcement for the paper "On uniform continuity of convex bodies with respect to measures in Banach spaces" by Anatolij Plichko.

Abstract: Let $\mu$ be a probability measure on a separable Banach space $X$. A subset $U\subset X$ is $\mu$-continuous if $\mu(\partial U)=0$. In the paper the $\mu$-continuity and uniform $\mu$-continuity of convex bodies in $X$, especially of balls and half-spaces, is considered. The $\mu$-continuity is interesting for study of the Glivenko-Cantelli theorem in Banach spaces. Answer to a question of F.~Tops{\o}e is given.

Archive classification: math.FA

Submitted from: aplichko@pk.edu.pl

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1208.6407

or

http://arXiv.org/abs/1208.6407