A conditional 0-1 law for the symmetric sigma-field
Probability
2007-05-23 v1
Abstract
Let (\Omega,\mathcal{B},P) be a probability space, \mathcal{A} a sub-sigma-field of \mathcal{B}, and \mu a regular conditional distribution for P given \mathcal{A}. For various, classically interesting, choices of \mathcal{A} (including tail and symmetric) the following 0-1 law is proved: There is a set A_0 in \mathcal{A} such that P(A_0)=1 and \mu(\omega)(A) is 0 or 1 for all A in \mathcal{A} and \omega in A_0. Provided \mathcal{B} is countably generated (and certain regular conditional distributions exist), the result applies whatever P is.
Keywords
Cite
@article{arxiv.0705.3028,
title = {A conditional 0-1 law for the symmetric sigma-field},
author = {Patrizia Berti and Pietro Rigo},
journal= {arXiv preprint arXiv:0705.3028},
year = {2007}
}
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9 pages