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has been cited by the following article:
TITLE: On the Differentiability of Vector Valued Additive Set Functions
AUTHORS: Mangatiana A. Robdera, Dintle Kagiso
KEYWORDS: Vector Valued Additive Set Function; Lebesgue-Radon-Nikodým Theorem; Fundamental Theorem of Calculus
JOURNAL NAME: Advances in Pure Mathematics, Vol.3 No.8, November 27, 2013
ABSTRACT: The Lebesgue-Nikodym Theorem states that for a Lebesgue measure an additive set function which is -absolutely continuous is the integral of a Lebegsue integrable a measurable function ; that is, for all measurable sets.Such a property is not shared by vector valued set functions. We introduce a suitable definition of the integral that will extend the above property to the vector valued case in its full generality. We also discuss a further extension of the Fundamental Theorem of Calculus for additive set functions with values in an infinite dimensional normed space.