Brascamp, Herm Jan; Lieb, Elliott H. On extensions of the Brunn-Minkowski and Prekopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation. (English) Zbl 0334.26009 J. Funct. Anal. 22, 366-389 (1976). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 17 ReviewsCited in 382 Documents MathOverflow Questions: Simple proof of Prékopa’s Theorem: log-concavity is preserved by marginalization MSC: 26D20 Other analytical inequalities 26A51 Convexity of real functions in one variable, generalizations 28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) PDF BibTeX XML Cite \textit{H. J. Brascamp} and \textit{E. H. Lieb}, J. Funct. Anal. 22, 366--389 (1976; Zbl 0334.26009) Full Text: DOI OpenURL References: [1] Lusternik, L, Die brunn-minkowskische ungleichung für beliebige messbare mengen, C. R. dokl. acad. sci. URSS no. 3, 8, 55-58, (1935) · Zbl 0012.27203 [2] Federer, M, Geometric measure theory, (1969), Springer New York · Zbl 0176.00801 [3] Prékopa, A, Logarithmic concave measures with application to stochastic programming, Acta sci. math. (Szeged), 32, 301-315, (1971) · Zbl 0235.90044 [4] Leindler, L, On a certain converse of Hölder’s inequality II, Acta sci. math. (Szeged), 33, 217-223, (1972) · Zbl 0245.26011 [5] Prékopa, A, On logarithmic concave measures and functions, Acta sci. math. (Szeged), 34, 335-343, (1973) · Zbl 0264.90038 [6] Brascamp, H.J; Lieb, E.H, Some inequalities for Gaussian measures, () · Zbl 0348.26011 [7] Brascamp, H.J; Lieb, E.H, Best constants in Young’s inequality, its converse and its generalization to more than three functions, Advances in math., 20, (1976) · Zbl 0339.26020 [8] Rinott, Y, On convexity of measures, (), to appear · Zbl 0347.60003 [9] Simon, B; Høegh-Krohn, R, Hypercontractive semigroups and two-dimensional self-coupled Bose fields, J. functional analysis, 9, 121-180, (1972) · Zbl 0241.47029 [10] Borell, C, Convex measures on locally convex spaces, Ark. mat., 12, 239-252, (1974), Note added in proof. After this paper was submitted for publication we discovered that Corollary 3.4 and its converse were proved by C. Borell: · Zbl 0297.60004 [11] Borell, C, Convex set functions, Period. math. hungar., 6, 111-136, (1975) · Zbl 0274.28009 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.