We present a straightforward introduction to the unconditional integrability in the extended sense. We state and proof useful necessary and sufficient conditions for unconditional integrability of complex or real valued functions. As an application, we obtain a simpler direct pro...
Open access
Research Article10.9734/ARJOM/2017/35466
We give extensions of the Lusin's Theorem, the Severini-Egorov's Theorem, and the Riesz Subsequence Theorems to the setting of a non-additive vector valued set functions and sequences of functions taking values in general metric spaces.
Open access
Research Article10.9734/ARJOM/2016/29547
A definitive positive answer to the so-called proper subspace problem (a.k.a. the atomic space problem) for quasi-normed spaces is given: every infinite dimensional quasi-normed space has a proper closed infinite-dimensional subspace.
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Research Article10.9734/ARJOM/2016/26927
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 obtain some representation theorems for the projective and in...
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Research Article10.9734/BJMCS/2015/17331
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.
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Research Article10.9734/BJMCS/2015/16752
We use tensor product to introduce a new approach to the theory of integration. Such an approach will strengthen the existing various classical concepts of integral and will provide a continuous thread tying the subject matter together. The integral of vector-valued functions wit...
Open access
Research Article10.9734/BJMCS/2014/12274