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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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Dual representation of monotone convex functions on $L^0$
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by Michael Kupper and Gregor Svindland PDF
Proc. Amer. Math. Soc. 139 (2011), 4073-4086 Request permission


We study monotone convex functions $\psi :{L}^0(\Omega ,\mathcal {F} ,\mathbb {P})\to (-\infty ,\infty ]$ and derive a dual representation as well as conditions that ensure the existence of a $\sigma$-additive subgradient. The results are motivated by applications in economic agents’ choice theory.
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Additional Information
  • Michael Kupper
  • Affiliation: Mathematics Institute, Humboldt University Berlin, Unter den Linden 6, D-10099 Berlin, Germany
  • MR Author ID: 736016
  • Email:
  • Gregor Svindland
  • Affiliation: École Polytechnique Fédérale de Lausanne, CDM SFI CSF - EXTRA 218, CH-1015 Lausanne, Switzerland
  • Address at time of publication: Department of Mathematics, University of Munich, Theresienstr. 39, D-80333 Munich, Germany
  • Email:,
  • Received by editor(s): April 22, 2010
  • Received by editor(s) in revised form: October 7, 2010
  • Published electronically: April 12, 2011
  • Additional Notes: The first author gratefully acknowledges financial support from the MATHEON project E.11
    The second author gratefully acknowledges support from Swissquote
  • Communicated by: Richard Rochberg
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 4073-4086
  • MSC (2010): Primary 46A16, 46A20, 49N15, 91G99
  • DOI:
  • MathSciNet review: 2823052