Now showing items 1-3 of 3
On the differentiability of vector valued additive set functions
(Scientific Research, http://www.scirp.org, 2013-11)
The Lebesgue-Nikodým Theorem states that for a Lebesgue measure λ:Σ〖⊂2〗^Ω→[0,∞) an additive set function F:Σ→R which is λ-absolutely continuous is the integral of a Lebegsue integrable a measurable function ...
On natural characterizations of tensor integrability
(Science Domain International, http://www.sciencedomain.org/, 2015-05-04)
We revisit the deﬁnition of the tensor integrability introduced in , and prove some useful characterizations that provide a foundation for studying relevant properties to the integration theory. As applications, we ...
On the Riesz representation theorem and integral operators
(NISC (Pty) Ltd, http://www.nisc.co.za/, 2015-12-14)
We present a Riesz representation theorem in the setting of extended integration theory as introduced in . The result is used to obtain boundedness theorems for integral operators in the more general setting of spaces ...