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

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.


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