Kluv\'{a}nek-Lewis-Henstock integral in a Banach space

Hemanta Kalita; Bipan Hazarika

Kluv\'{a}nek-Lewis-Henstock integral in a Banach space

Functional Analysis 2021-06-23 v1

Authors: Hemanta Kalita , Bipan Hazarika

Abstract

We investigate some properties and convergence theorem of Kluv\'{a}nek-Lewis-Henstock $\m-$ integrability for $\m-$ measurable functions that we introduced in \cite{ABH}. We give a $\m-$ a.e. convergence version of Dominated (resp. Bounded) Convergence Theorem for $\m.$ We introduce Kluv\'{a}nek-Lewis-Henstock integrable of scalar-valued functions with respect to a set valued measure in a Banach space. Finally we introduce $(KL)-$ type Dominated Convergence Theorem for the set-valued Kluv\'{a}nek-Lewis-Henstock integral.

Keywords

kluvanek-lewis-henstock integral banach space set-valued measure convergence theorem dominated convergence

Cite

@article{arxiv.2106.11778,
  title  = {Kluv\'{a}nek-Lewis-Henstock integral in a Banach space},
  author = {Hemanta Kalita and Bipan Hazarika},
  journal= {arXiv preprint arXiv:2106.11778},
  year   = {2021}
}

Comments

no of pages 16

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