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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Inequalities for $ \alpha$-optimal partitioning of a measurable space


Author: Jerzy Legut
Journal: Proc. Amer. Math. Soc. 104 (1988), 1249-1251
MSC: Primary 60A10; Secondary 28A99
MathSciNet review: 969055
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Abstract: An $ \alpha $-optimal partition $ \{ A_i^ * \} _{i = 1}^n$ of a measurable space according to $ n$ nonatomic probability measures $ \{ {\mu _i}\} _{i = 1}^n$ is defined. A two-sided inequality for $ {\nu ^ * } = \min \alpha _i^{ - 1}{\mu _i}(A_i^ * )$ is given. This estimation generalizes and improves a result of Elton et al. [3].


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0969055-4
PII: S 0002-9939(1988)0969055-4
Article copyright: © Copyright 1988 American Mathematical Society