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1. CJM 2005 (vol 57 pp. 961)

Borwein, Jonathan M.; Wang, Xianfu
Cone-Monotone Functions: Differentiability and Continuity
We provide a porosity-based approach to the differentiability and continuity of real-valued functions on separable Banach spaces, when the function is monotone with respect to an ordering induced by a convex cone $K$ with non-empty interior. We also show that the set of nowhere $K$-monotone functions has a $\sigma$-porous complement in the space of continuous functions endowed with the uniform metric.

Keywords:Cone-monotone functions, Aronszajn null set, directionally porous, sets, Gâteaux differentiability, separable space
Categories:26B05, 58C20

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