This is an announcement for the paper "The universal Glivenko-Cantelli property" by Ramon van Handel.

Abstract: Let F be a separable uniformly bounded family of measurable functions on a standard measurable space, and let N_{[]}(F,\epsilon,\mu) be the smallest number of \epsilon-brackets in L^1(\mu) needed to cover F. The following are equivalent: 1. F is a universal Glivenko-Cantelli class. 2. N_{[]}(F,\epsilon,\mu)<\infty for every \epsilon>0 and every probability measure \mu. 3. F is totally bounded in L^1(\mu) for every probability measure \mu. 4. F does not contain a Boolean \sigma-independent sequence. In particular, universal Glivenko-Cantelli classes are uniformity classes for general sequences of almost surely convergent random measures.

Archive classification: math.PR math.FA math.MG math.ST stat.TH

Mathematics Subject Classification: 60F15, 60B10, 41A46

Remarks: 15 pages

Submitted from: rvan@princeton.edu

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

http://front.math.ucdavis.edu/1009.4434

or

http://arXiv.org/abs/1009.4434