A concavity property for the measure of product sets in groups

• Autorzy: Imre Z. Ruzsa
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1991-1992
• Tom: 140
• Numer: 3
• Strony: 247-254

Daty

wydano

1992

otrzymano

1991-06-24

Twórcy

autor

Imre Z. Ruzsa

• Mathematical Institute, Hungarian Academy of Sciences, Budapest, Pf. 127, H-1364 Hungary

Bibliografia

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