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A class of null sets associated with convex functions on Banach spaces

Published online by Cambridge University Press:  17 April 2009

John Rainwater
John Rainwater
Affiliation:
Department of Mathematics GN-50, University of Washington Seattle, WA 98195, United States of America
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Abstract

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A generalisation of the notion of “sets of measure zero” for arbitrary Banach spaces is defined so that continuous convex functions are automatically Gateaux differentiable “almost everywhere”. It is then shown that this class of sets satisfies all the properties tht one expects of sets of measure zero. Moreover (in a certain large class of Banach spaces, at least) nonempty open sets are not of “measure zero”.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 42 , Issue 2 , October 1990 , pp. 315 - 322
Copyright
Copyright © Australian Mathematical Society 1990

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