NON-DIFFERENTIABLE INDEFINITE PETTIS INTEGRALS

Original Articles

NON-DIFFERENTIABLE INDEFINITE PETTIS INTEGRALS

Published in: Quaestiones Mathematicae
Volume 17 , issue 2 , 1994 , pages: 137–139
DOI: 10.1080/16073606.1994.9631753
Author(s): V.M. Kadets Department of Mechanics and Mathematics, Ukraine
Keywords: 46G10 , 46340 , 46G05
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Abstract

Answering a question posed by J. Diestel we construct for every infinite-dimensional Banach space X an X-valued Pettis integrable function f on [0,1] for which F(t) = ∫t 0 f(x)dx is non-differentiable on a set of positive measure.
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