A Gaussian Correlation Inequality for Symmetric Convex Sets
Pitt, Loren D.
Ann. Probab., Tome 5 (1977) no. 6, p. 470-474 / Harvested from Project Euclid
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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 $$\int_{A\cap B}\mathbf{n}(x) d^2x \geqq (\int_A \mathbf{n}(x) d^2x)(\int_B \mathbf{n}(x) d^2x).$$
Publié le : 1977-06-14
Classification:  Quasi-concave functions,  convex sets,  correlation inequalities,  60G15,  26A51 
@article{1176995808,
     author = {Pitt, Loren D.},
     title = {A Gaussian Correlation Inequality for Symmetric Convex Sets},
     journal = {Ann. Probab.},
     volume = {5},
     number = {6},
     year = {1977},
     pages = { 470-474},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176995808}
}

Pitt, Loren D. A Gaussian Correlation Inequality for Symmetric Convex Sets. Ann. Probab., Tome 5 (1977) no. 6, pp.  470-474. http://gdmltest.u-ga.fr/item/1176995808/