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Now showing items 1-10 of 15

#### A concise approach to real analysis

(Lulu, www.lulu.com, 2014-10-07)

#### 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 summable bases in Banach spaces

(Science Domian International, www.sciencedomain.org, 2014-06-24)

We introduce the notion of summable bases that naturally generalizes the notion of unconditional sequence bases for Banach spaces. We shall be particularly interested in some classical results on sequences and series in ...

#### On the Orlicz-Pettis theorem for integrals

(Pushpa Publishing House, www.pphmj.com, 2010-10)

In this note, we propose a more efficient approach to the definition of the integral of Banach-valued functions that enables us to give an improved version of the Orlicz-Pettis theorem for integrals.

#### A new general approach to vector valued stochastic integration

(International Journal of Modeling and Optimization, www.ijmo.org, 2014-08)

We use an extended theory of integral that generalizes the integration of vector valued functions with respect to non-negative, monotonic,countably subadditive set functions, in order to introduce a new approach to stochastic ...

#### Unified approach to vector valued integration

(Pushpa Publishing House, www.pphmj.com, 2013-06)

We introduce a natural and more flexible approach to the definition of vector valued integral that will completely forgo any measurability assumption, strengthen the existing various classical concepts of ...

#### 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 ...

#### More on equivalence properties of Radon-Nikodym property types and Complete Continuity property types

(Pushpa Publishing House, www.pphmj.com, 2013-01)

We study the equivalence property of the I- and II-L-Radon-Nikodým property (resp. I- and II-L-complete continuity property) types of Banach spaces. As a by-product, we obtain a proof of the following: F. Lust-Picard’s ...

#### 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 ...