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Partitioning General Probability Measures
The Annals of Probability
  • Theodore P. Hill, Georgia Institute of Technology - Main Campus
Publication Date
Suppose μ1, ..., μn are probability measures on the same measurable space (Ω, F). Then if all atoms of each μi have mass α or less, there is a measurable partition A1,..., An of Ω so that μi(Ai) ≥ Vn(α) for all i = 1, ... , n, where Vn(•) is an explicitly given piecewise linear nonincreasing continuous function on [0, 1]. Moreover, the bound Vn(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.
Citation Information
Theodore P. Hill. "Partitioning General Probability Measures" The Annals of Probability Vol. 15 Iss. 2 (1987) p. 804 - 813
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