A note on the Ehrhard inequality

Latała, Rafał

Latała, Rafał

Studia Mathematica, Tome 119 (1996), p. 169-174 / Harvested from The Polish Digital Mathematics Library

Résumé

We prove that for λ ∈ [0,1] and A, B two Borel sets in $ℝ^{n}$ with A convex, $Φ^{- 1} (γ_{n} (λ A + (1 - λ) B)) \geq λ Φ^{- 1} (γ_{n} (A)) + (1 - λ) Φ^{- 1} (γ_{n} (B))$ , where $γ_{n}$ is the canonical gaussian measure in $ℝ^{n}$ and $Φ^{- 1}$ is the inverse of the gaussian distribution function.

Publié le : 1996-01-01

Zbl 0847.60012

EUDML-ID : urn:eudml:doc:216271

@article{bwmeta1.element.bwnjournal-article-smv118i2p169bwm,
     author = {Rafa\l\ Lata\l a},
     title = {A note on the Ehrhard inequality},
     journal = {Studia Mathematica},
     volume = {119},
     year = {1996},
     pages = {169-174},
     zbl = {0847.60012},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv118i2p169bwm}
}

Latała, Rafał. A note on the Ehrhard inequality. Studia Mathematica, Tome 119 (1996) pp. 169-174. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv118i2p169bwm/

Bibliographie

[00000] [1] A. Ehrhard, Symétrisation dans l'espace de Gauss, Math. Scand. 53 (1983), 281-301. | Zbl 0542.60003

[00001] [2] M. Ledoux and M. Talagrand, Probability in Banach Spaces, Springer, 1991.