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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
Abstract
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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