Fréchet differentiation of convex functions in a Banach space with a separable dual
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- by D. Preiss and L. Zajíček PDF
- Proc. Amer. Math. Soc. 91 (1984), 202-204 Request permission
Abstract:
Let $X$ be a real Banach space with a separable dual and let $f$ be a continuous convex function on $X$. We sharpen the well-known result that the set of points at which $f$ is not Fréchet differentiable is a first category set by showing that it is even $\sigma$-porous. On the other hand, a simple example shows that this set need not be a null set for any given Radon measure.References
- Edgar Asplund, Fréchet differentiability of convex functions, Acta Math. 121 (1968), 31–47. MR 231199, DOI 10.1007/BF02391908
- Luděk Zajíček, Sets of $\sigma$-porosity and sets of $\sigma$-porosity $(q)$, Časopis Pěst. Mat. 101 (1976), no. 4, 350–359 (English, with Loose Russian summary). MR 0457731
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 91 (1984), 202-204
- MSC: Primary 46G05
- DOI: https://doi.org/10.1090/S0002-9939-1984-0740171-1
- MathSciNet review: 740171