# A note on the Ehrhard inequality

Studia Mathematica (1996)

• Volume: 118, Issue: 2, page 169-174
• ISSN: 0039-3223

top

## Abstract

top
We prove that for λ ∈ [0,1] and A, B two Borel sets in ${ℝ}^{n}$ with A convex, ${\Phi }^{-1}\left({\gamma }_{n}\left(\lambda A+\left(1-\lambda \right)B\right)\right)\ge \lambda {\Phi }^{-1}\left({\gamma }_{n}\left(A\right)\right)+\left(1-\lambda \right){\Phi }^{-1}\left({\gamma }_{n}\left(B\right)\right)$, where ${\gamma }_{n}$ is the canonical gaussian measure in ${ℝ}^{n}$ and ${\Phi }^{-1}$ is the inverse of the gaussian distribution function.

## How to cite

top

Latała, Rafał. "A note on the Ehrhard inequality." Studia Mathematica 118.2 (1996): 169-174. <http://eudml.org/doc/216271>.

@article{Latała1996,
abstract = {We prove that for λ ∈ [0,1] and A, B two Borel sets in $ℝ^n$ with A convex, $Φ^\{-1\}(γ_n(λA + (1-λ)B)) ≥ λΦ^\{-1\}(γ_n(A)) + (1-λ)Φ^\{-1\}(γ_n(B))$, where $γ_n$ is the canonical gaussian measure in $ℝ^n$ and $Φ^\{-1\}$ is the inverse of the gaussian distribution function.},
author = {Latała, Rafał},
journal = {Studia Mathematica},
keywords = {inverse of the Gaussian distribution function},
language = {eng},
number = {2},
pages = {169-174},
title = {A note on the Ehrhard inequality},
url = {http://eudml.org/doc/216271},
volume = {118},
year = {1996},
}

TY - JOUR
AU - Latała, Rafał
TI - A note on the Ehrhard inequality
JO - Studia Mathematica
PY - 1996
VL - 118
IS - 2
SP - 169
EP - 174
AB - We prove that for λ ∈ [0,1] and A, B two Borel sets in $ℝ^n$ with A convex, $Φ^{-1}(γ_n(λA + (1-λ)B)) ≥ λΦ^{-1}(γ_n(A)) + (1-λ)Φ^{-1}(γ_n(B))$, where $γ_n$ is the canonical gaussian measure in $ℝ^n$ and $Φ^{-1}$ is the inverse of the gaussian distribution function.
LA - eng
KW - inverse of the Gaussian distribution function
UR - http://eudml.org/doc/216271
ER -

top

## NotesEmbed?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.