A note on the "conditional triviality" property for regular conditional distributions

Julian Newman

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arXiv · 1511.08864

A note on the "conditional triviality" property for regular conditional distributions

Julian Newman

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Abstract

We make the simple, and yet deep, observation that a regular conditional distribution (rcd) almost surely trivialises the conditioning $σ$-algebra if and only if there exists a "measurable selection" of regular conditional distributions for almost all the measures arising out of the original rcd.

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Julian Newman. 2015-11-28. A note on the "conditional triviality" property for regular conditional distributions. https://arxiv.org/abs/1511.08864

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