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

 

A new proof of the integrability of the subdifferential of a convex function on a Banach space


Authors: Milen Ivanov and Nadia Zlateva
Journal: Proc. Amer. Math. Soc. 136 (2008), 1787-1793
MSC (2000): Primary 52A41, 49J53; Secondary 26E15, 47H05
Published electronically: January 30, 2008
MathSciNet review: 2373609
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Abstract: We provide a simple proof of the Moreau-Rockafellar theorem that a proper lower semicontinuous convex function on a Banach space is determined up to a constant by its subdifferential.


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Additional Information

Milen Ivanov
Affiliation: Faculty of Mathematics and Informatics, University of Sofia, 5, James Bourchier Blvd., 1164 Sofia, Bulgaria
Email: milen@fmi.uni-sofia.bg

Nadia Zlateva
Affiliation: Faculty of Mathematics and Informatics, University of Sofia, 5, James Bourchier Blvd., 1164 Sofia, Bulgaria
Email: zlateva@fmi.uni-sofia.bg

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09178-8
PII: S 0002-9939(08)09178-8
Keywords: Convex function, subdifferential
Received by editor(s): January 8, 2007
Published electronically: January 30, 2008
Additional Notes: The first author was supported in part by the Research and Development Fund of Sofia University, Contract # 22/2006; and by NSFR of Bulgaria, Contract # 401/2004.
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.