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June, 1979 Existence of Independent Complements in Regular Conditional Probability Spaces
D. Ramachandran
Ann. Probab. 7(3): 433-443 (June, 1979). DOI: 10.1214/aop/1176995044

Abstract

Let $(X, \mathscr{A}, P)$ be a probability space and $\mathscr{B}$ a sub-$\sigma$-algebra of $\mathscr{A}$. Some results on regular conditional probabilities given $\mathscr{B}$ are proved. Using these, when $\mathscr{A}$ is separable and $\mathscr{B}$ is a countably generated sub-$\sigma$-algebra of $\mathscr{A}$ such that there is a regular conditional probability given $\mathscr{B}$, necessary and sufficient conditions for the existence of an independent complement for $\mathscr{B}$ are given.

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D. Ramachandran. "Existence of Independent Complements in Regular Conditional Probability Spaces." Ann. Probab. 7 (3) 433 - 443, June, 1979. https://doi.org/10.1214/aop/1176995044

Information

Published: June, 1979
First available in Project Euclid: 19 April 2007

zbMATH: 0399.28001
MathSciNet: MR528321
Digital Object Identifier: 10.1214/aop/1176995044

Subjects:
Primary: 28A05
Secondary: 28A20, 28A25, 28A35

Rights: Copyright © 1979 Institute of Mathematical Statistics

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Vol.7 • No. 3 • June, 1979
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