Geodesic
A concavity property for the measure of product sets in groups
Fundamenta Mathematicae, Tome 140 (1991) no. 3, pp. 247-254

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/fm-140-3-247-254

Imre Ruzsa 1

1 
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Imre Ruzsa. A concavity property for the measure of product sets in groups. Fundamenta Mathematicae, Tome 140 (1991) no. 3, pp. 247-254. doi: 10.4064/fm-140-3-247-254

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