Now showing items 1-15 of 15

  • A concise approach to real analysis 

    Robdera, Mangatiana A. (Lulu,, 2014-10-07)
  • Extensions of the Lusin's Theorem, the Severini-Egorov's Theorem and the Riesz Subsequence Theorems 

    Robdera, Mangatiana A. (ScienceDomain International;, 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 ...
  • More on equivalence properties of Radon-Nikodym property types and Complete Continuity property types 

    Robdera, Mangatiana A. (Pushpa Publishing House,, 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 ...
  • A new general approach to vector valued stochastic integration 

    Robdera, Mangatiana A. (International Journal of Modeling and Optimization,, 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 ...
  • On cartesian nets and fubini-tonelli type theorem 

    Robdera, Mangatiana A. (International Journal of Applied Physics and Mathematics,, 2017-04)
    The notion of Cartesian net is introduced in order to provide an appropriate setting for the notion of double limit for directed functions defined on Cartesian products of spaces. As an application, we obtain extensions ...
  • On natural characterizations of tensor integrability 

    Robdera, Mangatiana A. (Science Domain International,, 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 non-metric covering lemmas and extended Lebesgue-differentiation theorem 

    Robdera, Mangatiana A. (Science Domain International;, 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 size function topology and fixed point theorems 

    Robdera, Mangatiana A. (International Scientific Publications and Consulting Services,, 2017-06)
    In this paper, we introduce and study a metric-like (non-necessarily metric) topology that is weaker than the original topology of a given topological space. The results are used to provide more useful and more general ...
  • On summable bases in Banach spaces 

    Robdera, Mangatiana A. (Science Domian International,, 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 differentiability of vector valued additive set functions 

    Robdera, Mangatiana A.; Kagiso, Dintle (Scientific Research,, 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 the Orlicz-Pettis theorem for integrals 

    Robdera, Mangatiana A. (Pushpa Publishing House,, 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.
  • On the Riesz representation theorem and integral operators 

    Robdera, Mangatiana A. (NISC (Pty) Ltd,, 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 ...
  • On the subspace problem for Quasi-normed spaces 

    Robdera, Mangatiana A. (ScienceDomain International;, 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 ...
  • A unified approach to integration theory 

    Robdera, Mangatiana A. (International Journal of Applied Physics and Mathematics,, 2019-01)
    We investigate the common features and the resemblance of the central parts of the different existing integration theories to obtain a more unified approach to the notion of integral. Our approach gives a presentation of ...
  • Unified approach to vector valued integration 

    Robdera, Mangatiana A. (Pushpa Publishing House,, 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 ...