A concavity property for the measure of product sets in groups

Volume 140 / 1992

Imre Ruzsa Fundamenta Mathematicae 140 (1992), 247-254 DOI: 10.4064/fm-140-3-247-254


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 $μ̲(AB) ≥ min (μ̲(A) + μ̲(B), μ(G))$ for unimodular G.


  • Imre Ruzsa

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