On conditions of differentiability almost everywhere for absolutely continuous Banach-valued functions. (English. Russian original) Zbl 0961.26012

Solodov, A. P.

Mosc. Univ. Math. Bull. 54, No. 4, 29-32 (1999); translation from Vestn. Mosk. Univ., Ser I 1999, No. 4, 50-53 (1999).

In this note the author considers absolutely continuous functions specified on a direct line segment which take their values in a Banach space. The author establishes the relationship between the differentiability almost everywhere of absolutely continuous functions and the convergence in variation. A new condition under which the Lebesgue theorem holds true is formulated as a corollary.

Reviewer: V. I. Zhukovskij (Moskva)

MSC:

26E20	Calculus of functions taking values in infinite-dimensional spaces
46G05	Derivatives of functions in infinite-dimensional spaces
28B05	Vector-valued set functions, measures and integrals

Keywords:

continuous Banach-valued function; conditions of differentiability almost everywhere; absolutely continuous functions