On the Differentiability of Vector Valued Additive Set Functions

DOI: 10.4236/apm.2013.38087   PDF   HTML     2,250 Downloads   3,937 Views   Citations

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.

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M. Robdera and D. Kagiso, "On the Differentiability of Vector Valued Additive Set Functions," Advances in Pure Mathematics, Vol. 3 No. 8, 2013, pp. 653-659. doi: 10.4236/apm.2013.38087.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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