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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the improvement of concavity of convex measures
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by Arnaud Marsiglietti PDF
Proc. Amer. Math. Soc. 144 (2016), 775-786 Request permission


We prove that a general class of measures, which includes $\log$-concave measures, is $\frac {1}{n}$-concave according to the terminology of Borell, with additional assumptions on the measures or on the sets, such as symmetries. This generalizes results of Gardner and Zvavitch published in 2010.
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Additional Information
  • Arnaud Marsiglietti
  • Affiliation: Université Paris-Est, LAMA (UMR 8050), UPEMLV, UPEC, CNRS, F-77454, Marne-la-Vallée, France
  • MR Author ID: 1063405
  • Email:
  • Received by editor(s): April 4, 2014
  • Received by editor(s) in revised form: December 12, 2014
  • Published electronically: June 24, 2015
  • Additional Notes: The author was supported in part by the Agence Nationale de la Recherche, project GeMeCoD (ANR 2011 BS01 007 01).
  • Communicated by: Thomas Schlumprecht
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 775-786
  • MSC (2010): Primary 52A20, 52A40; Secondary 28A75, 60G15
  • DOI:
  • MathSciNet review: 3430853