Partitioning General Probability MeasuresThe Annals of Probability
AbstractSuppose 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 InformationTheodore P. Hill. "Partitioning General Probability Measures" The Annals of Probability Vol. 15 Iss. 2 (1987) p. 804 - 813
Available at: http://works.bepress.com/tphill/21/