Title

Partitioning General Probability Measures

Author Info

Theodore P. Hill, Georgia Institute of Technology - Main CampusFollow

Recommended Citation

Published in The Annals of Probability, Volume 15, Issue 2, April 1, 1987, pages 804-813.

Copyright © 1987 Institute of Mathematical Statistics.

NOTE: At the time of publication, the author Theodore P. Hill was not yet affiliated with Cal Poly.

The definitive version is available at https://doi.org/10.1214/aop/1176992173.

Abstract

Suppose μ₁, ..., μ_n are probability measures on the same measurable space (Ω, F). Then if all atoms of each μ_i have mass α or less, there is a measurable partition A₁,..., A_n of Ω so that μ_i(A_i) ≥ V_n(α) for all i = 1, ... , n, where V_n(•) is an explicitly given piecewise linear nonincreasing continuous function on [0, 1]. Moreover, the bound V_n(α) is attained for all n and all α. Applications are given to L₁ spaces, to statistical decision theory, and to the classical nonatomic case.

Disciplines

Mathematics