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

Research paper by Julian Newman

Indexed on: 27 Nov '15Published on: 27 Nov '15Published in: Mathematics - Probability



Abstract

We make the simple, and yet deep, observation that a regular conditional distribution (rcd) almost surely trivialises the conditioning $\sigma$-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.