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June, 1977 A Gaussian Correlation Inequality for Symmetric Convex Sets
Loren D. Pitt
Ann. Probab. 5(3): 470-474 (June, 1977). DOI: 10.1214/aop/1176995808

Abstract

If $n(x)$ is the standard normal density on $R^2$ and if $A = -A$ and $B = -B$ are convex subsets of $R^2$ then $$\int_{A\cap B}\mathbf{n}(x) d^2x \geqq (\int_A \mathbf{n}(x) d^2x)(\int_B \mathbf{n}(x) d^2x).$$

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Loren D. Pitt. "A Gaussian Correlation Inequality for Symmetric Convex Sets." Ann. Probab. 5 (3) 470 - 474, June, 1977. https://doi.org/10.1214/aop/1176995808

Information

Published: June, 1977
First available in Project Euclid: 19 April 2007

zbMATH: 0359.60018
MathSciNet: MR448705
Digital Object Identifier: 10.1214/aop/1176995808

Subjects:
Primary: 60G15
Secondary: 26A51‎

Rights: Copyright © 1977 Institute of Mathematical Statistics

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Vol.5 • No. 3 • June, 1977
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