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

 

Separable determination
of integrability and minimality
of the Clarke subdifferential mapping


Authors: Jonathan M. Borwein and Warren B. Moors
Journal: Proc. Amer. Math. Soc. 128 (2000), 215-221
MSC (1991): Primary 49J52, 46N10; Secondary 58C20
Published electronically: September 9, 1999
MathSciNet review: 1622793
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we show that the study of integrability and $D$-representability of Lipschitz functions defined on arbitrary Banach spaces reduces to the study of these properties on separable Banach spaces.


References [Enhancements On Off] (What's this?)

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  • 2. Jonathan M. Borwein and Warren B. Moors, Essentially smooth Lipschitz functions, J. Funct. Anal. 149 (1997), no. 2, 305–351. MR 1472362 (98i:58028), http://dx.doi.org/10.1006/jfan.1997.3101
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  • 6. Jens Peter Reus Christensen, On sets of Haar measure zero in abelian Polish groups, Proceedings of the International Symposium on Partial Differential Equations and the Geometry of Normed Linear Spaces (Jerusalem, 1972), 1972, pp. 255–260 (1973). MR 0326293 (48 #4637)
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Additional Information

Jonathan M. Borwein
Affiliation: CECM, Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
Email: jborwein@cecm.sfu.ca

Warren B. Moors
Affiliation: Department of Mathematics, University of Waikato, Private Bag 3105, Hamilton, New Zealand
Email: moors@math.waikato.ac.nz

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05001-7
PII: S 0002-9939(99)05001-7
Keywords: Separable reduction, integrability, $D$-representability, minimal cusco.
Received by editor(s): October 22, 1997
Received by editor(s) in revised form: March 18, 1998
Published electronically: September 9, 1999
Additional Notes: The first author’s research was supported by NSERC and the Shrum Endowment at Simon Fraser University.
Communicated by: Dale Alspach
Article copyright: © Copyright 1999 American Mathematical Society