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On non-metric covering lemmas and extended Lebesgue-differentiation theorem
(Science Domain International;http://www.sciencedomain.org, 2015-03-28)
We give a non-metric version of the Besicovitch Covering Lemma and an extension of the
Lebesgue-Differentiation Theorem into the setting of the integration theory of vector valued
functions.
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 [1], 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 [6]. The result is used to obtain boundedness theorems for integral operators in the more general setting of spaces ...
Some relations between admissible monomials for the polynomial algebra
(Hindawi Publishing Corporation, www.Hindawi.com, 2015)
Let P(𝑛) = F2[𝑥1, . . . , 𝑥𝑛] be the polynomial algebra in 𝑛 variables 𝑥𝑖, of degree one, over the field F2 of two elements. The mod-2 Steenrod algebra A acts on P(𝑛) according to well known rules. A major problem ...