A spherical surface measure inequality for convex sets-Reference-Cited by-同舟云学术

A spherical surface measure inequality for convex sets

Published:1972 Issue:1 Volume:33 Page:114-119
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Fefferman Charles,Jodeit Max,Perlman Michael D.

Abstract

Let the set C in the Euclidean space of n dimensions be closed, symmetric under reflection in the origin, and convex. The portion of the surface of the unit ball lying in C is shown to decrease in (the uniform) surface measure when C is replaced by AC, the image of C under any linear transformation A with norm no greater than one. Some cases of equality are discussed, and an application is given.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1972-033-01/S0002-9939-1972-0293500-1/S0002-9939-1972-0293500-1.pdf

Reference4 articles.

1. The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities;Anderson, T. W.;Proc. Amer. Math. Soc.,1955

2. On seminorms and probabilities, and abstract Wiener spaces;Dudley, R. M.;Ann. of Math. (2),1971

3. Measurable functions on Hilbert space;Gross, Leonard;Trans. Amer. Math. Soc.,1962

4. A theorem on convex sets with applications;Sherman, S.;Ann. Math. Statist.,1955

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