A concavity property for the measure of product sets in groups

Abstract

Let G be a connected locally compact group with a left invariant Haar measure μ. We prove that the function ξ(x) = inf {μ̅(AB): μ(A) = x} is concave for any fixed bounded set B ⊂ G. This is used to give a new proof of Kemperman's inequality $μ̲(AB) ≥ min

Locations

• Fundamenta Mathematicae - View - PDF