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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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