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