Borell, Christer Convex set functions in d-space. (English) Zbl 0307.28009 Period. Math. Hung. 6, 111-136 (1975). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 69 Documents MSC: 28A10 Real- or complex-valued set functions 26A51 Convexity of real functions in one variable, generalizations PDFBibTeX XMLCite \textit{C. Borell}, Period. Math. Hung. 6, 111--136 (1975; Zbl 0307.28009) Full Text: DOI References: [1] T. W. Anderson, The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities,Proc. Amer. Math. Soc. 6 (1955), 170–176. · Zbl 0066.37402 [2] C. Borell, Inverse inequalities for concave or generalized concave functions, Uppsala Univ. Dept. of Math., Report No. 44 (1972). [3] C. Borell, Complements of Lyapunov’s inequality,Math. Ann. 205 (1973), 323–331. · Zbl 0255.26011 [4] S. Das Gupta, M. L. Eaton, I. Olkin, M. Perlman, L. J. Savage andM. Sobel, Inequalities on the probability content of convex regions for elliptically contoured distributions,Proc. Sixth Berkeley Sympos. Math. Statist. Probability, Vol. II, Berkeley, 1972, 241–265. · Zbl 0253.60021 [5] A. Dinghas, Über eine Klasse superadditiver Mengenfunktionale von Brunn-Minkowski-Lusternikschem typus,Math. Z. 68 (1957/58), 111–125. · Zbl 0083.38301 [6] H. Hadwiger andD. Ohman, Brunn-Minkowskischer Satz und Isoperimetrie,Math. Z. 66 (1956/57), 1–8. · Zbl 0071.38001 [7] N. L. Johnson andS. Kotz,Distributions in Statistics: Continuous Multivariate Distributions, Wiley, New York, 1972. · Zbl 0248.62021 [8] L. Leindler, On a certain converse of Hölder’s inequality II,Acta Sci. Math. (Szeged) 33 (1972), 215–223. · Zbl 0245.26011 [9] P. Montel, Sur les fonctions convexes et les fonctions sousharmoniques,J. Math. Pures Appl. 7 (1928), 29–60. · JFM 54.0517.01 [10] A. Prékopa, Logarithmic concave measures with application to stochastic programming,Acta Sci. Math. (Szeged) 32 (1971), 301–316. · Zbl 0235.90044 [11] C. A. Rogers andG. C. Shephard, The difference body of a convex body,Arch. Math. (Basel) 8 (1957), 220–233. · Zbl 0082.15703 [12] R. A. Rosenbaum, Sub-additive functions,Duke Math. J. 17 (1950), 225–247. · Zbl 0038.06603 [13] W. Rudin,Real and Complex Analysis, McGraw-Hill, New York, 1966. · Zbl 0142.01701 [14] I. J. Schoenberg, On Pólya frequency functions I. The totally positive functions and their Laplace transforms,J. Analyse Math. 1 (1951), 331–374. · Zbl 0045.37602 [15] S. Sherman, A theorem on convex sets with applications,Ann. Math. Statist. 26 (1955), 763–767. · Zbl 0066.37403 [16] W. Sierpiński, Sur la question de la mesurabilité de la base de M. Hamel,Fund. Math. 1 (1920), 105–111. · JFM 47.0180.03 [17] S. Vajda,Probabilistic programming, Academic Press, New York, 1972. 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.