## Stepanoff’s theorem in separable Banach spaces.(English)Zbl 0937.46038

The following generalization of a Stepanoff’s theorem (1923) is proved:
Let $$X$$ be a separable Banach space, and let $$Y$$ be a Banach space with Radon-Nikodým property (that is, every $$Y$$-valued function of bounded variation on the interval [0,1] is differentiable almost everywhere on this interval). Then for any mapping $$f:X\rightarrow Y$$ there exists an exceptional in the sense of Aronszajn (1976) set $$E$$, such that $$f$$ is Gateaux differentiable at every point of $$L\setminus E$$, $$L$$ being the set of all points where $$f$$ is Lipschitz.
Reviewer: V.Averbuch (Opava)

### MSC:

 46G05 Derivatives of functions in infinite-dimensional spaces
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