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.
Cite this paper
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
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