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Journal of Convex Analysis 27 (2020), No. 1, 031--048
Copyright Heldermann Verlag 2020

Interval-Decomposability of Continuous Functions, and Convexity

Zvi Artstein
Dept. of Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel

A generalization of the notion of a decomposable set of functions is offered. It applies, in particular, to continuous functions which are not differentiable. Following the classical analysis of decomposable families of integrable functions, it is shown that many convex analysis features hold also in the general framework.

Keywords: Interval-decomposable sets, decomposed hull, attainable set.

MSC: 28B20, 54C60.

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