On Convexity of Measures
Rinott, Yosef
Ann. Probab., Tome 4 (1976) no. 6, p. 1020-1026 / Harvested from Project Euclid
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A simple geometric proof and some applications are given to results of C. Borell providing necessary and sufficient conditions that a density in $R^n$ generates a measure satisfying a convexity property of the type $$P(\theta A_0 + (1 - \theta)A_1) \geqq \{\theta\lbrack P(A_0)\rbrack^s + (1 - \theta)\lbrack P(A_1) \rbrack^s\}^{1/s}.$$
Publié le : 1976-12-14
Classification:  Convexity,  Brunn-Minkowski inequality,  62E10,  62H10,  26A51,  26A86 
@article{1176995947,
     author = {Rinott, Yosef},
     title = {On Convexity of Measures},
     journal = {Ann. Probab.},
     volume = {4},
     number = {6},
     year = {1976},
     pages = { 1020-1026},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176995947}
}

Rinott, Yosef. On Convexity of Measures. Ann. Probab., Tome 4 (1976) no. 6, pp.  1020-1026. http://gdmltest.u-ga.fr/item/1176995947/