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On the subspace problem for Quasi-normed spaces
(ScienceDomain International; www.sciencedomain.org, 2016-07-02)
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 ...
Extensions of the Lusin's Theorem, the Severini-Egorov's Theorem and the Riesz Subsequence Theorems
(ScienceDomain International; www.sciencedomain.org, 2016-10-14)
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 ...