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December, 1976 On Convexity of Measures
Yosef Rinott
Ann. Probab. 4(6): 1020-1026 (December, 1976). DOI: 10.1214/aop/1176995947

Abstract

A simple geometric proof and some applications are given to results of C. Borell providing necessary and sufficient conditions that a density in $R^n$ generates a measure satisfying a convexity property of the type $$P(\theta A_0 + (1 - \theta)A_1) \geqq \{\theta\lbrack P(A_0)\rbrack^s + (1 - \theta)\lbrack P(A_1) \rbrack^s\}^{1/s}.$$

Citation

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Yosef Rinott. "On Convexity of Measures." Ann. Probab. 4 (6) 1020 - 1026, December, 1976. https://doi.org/10.1214/aop/1176995947

Information

Published: December, 1976
First available in Project Euclid: 19 April 2007

zbMATH: 0347.60003
MathSciNet: MR428540
Digital Object Identifier: 10.1214/aop/1176995947

Subjects:
Primary: 62E10
Secondary: 26A51‎, 26A86, 62H10

Rights: Copyright © 1976 Institute of Mathematical Statistics

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Vol.4 • No. 6 • December, 1976
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