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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Dual representation of monotone convex functions on $ L^0$


Authors: Michael Kupper and Gregor Svindland
Journal: Proc. Amer. Math. Soc. 139 (2011), 4073-4086
MSC (2010): Primary 46A16, 46A20, 49N15, 91G99
Published electronically: April 12, 2011
MathSciNet review: 2823052
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Abstract: 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
Email: kupper@math.hu-berlin.de

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: gregor.svindland@epfl.ch, svindla@math.lmu.de

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10835-9
PII: S 0002-9939(2011)10835-9
Keywords: Monotone convex function, duality, subgradient, bipolar representation
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
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.