A class of null sets associated with convex functions on Banach spaces
- 1 October 1990
- journal article
- research article
- Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society
- Vol. 42 (2) , 315-322
- https://doi.org/10.1017/s000497270002846x
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”.Keywords
This publication has 7 references indexed in Scilit:
- Convex Functions, Monotone Operators and DifferentiabilityLecture Notes in Mathematics, 1989
- Negligible sets in locally convex spacesMathematical Notes, 1984
- Gateaux Differentiability of Convex Functions on Banach SpacesJournal of the London Mathematical Society, 1979
- Gaussian null sets and differentiability of Lipschitz map on Banach spacesPacific Journal of Mathematics, 1978
- Differentiability of Lipschitzian mappings between Banach spacesStudia Mathematica, 1976
- On the differentiability of Lipschitz mappings in Fréchet spacesStudia Mathematica, 1973
- Sur l'ensemble des points de non-dérivabilité d'une fonction continueBulletin de la Société Mathématiques de France, 1946