English

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

Probability 2015-12-01 v1

Abstract

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

Cite

@article{arxiv.1511.08864,
  title  = {A note on the "conditional triviality" property for regular conditional distributions},
  author = {Julian Newman},
  journal= {arXiv preprint arXiv:1511.08864},
  year   = {2015}
}
R2 v1 2026-06-22T11:56:04.879Z