On a class of integral inequalities and their measure-theoretic consequences

DOI10.1016/0022-247X(80)90136-5zbMath0442.26011MaRDI QIDQ1143515

S. H. Smith

Publication date: 1980

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

isoperimetric inequalityintegral inequalitiesBonnesen- Fenchel inequalityBrunn-Minkowski-Lusternik inequalityHanstock-Macbeath-Dinghas inequalitymeasure generated by concave function

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Length, area, volume, other geometric measure theory (28A75) Inequalities for sums, series and integrals (26D15) Random convex sets and integral geometry (aspects of convex geometry) (52A22)

Related Items

The Brunn-Minkowski inequality, Convex bodies and norms associated to convex measures, Strict power concavity of a convolution, Every convex body has a unique illuminating center, Brunn-Minkowski inequalities in product metric measure spaces, Inverse additive problems for Minkowski sumsets. II, On the framework of \(L_p\) summations for functions, Quermassintegrals of quasi-concave functions and generalized Prékopa-Leindler inequalities, From Brunn-Minkowski to sharp Sobolev inequalities, Stability analysis for stochastic programs, Equality in Borell-Brascamp-Lieb inequalities on curved spaces, On the improvement of concavity of convex measures, The Brunn-Minkowski inequality, Minkowski's first inequality, and their duals

Cites Work

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• On convexity of measures
• Some estimations useful in geometry of numbers
• Convex set functions in \(d\)-space
• On some inequalities of series of positive terms
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• The Integral of a Symmetric Unimodal Function over a Symmetric Convex Set and Some Probability Inequalities
• On the Measure of Sum-Sets. (I) The Theorems of Brunn, Minkowski, and Lusternik
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