Kurzweil-Henstock Integral in Riesz spaces

Indexed in: Scopus, EBSCO.

This Ebook is concerned with both the theory of the Kurzweil-Henstock integral and the basic facts on Riesz spaces. Moreover, even the so-called Šipoš integral, which has several applications in ...
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Pettis-type Approach

Pp. 166-177 (12)

Antonio Boccuto, Beloslav Riecan and Marta Vrabelova

Abstract

In this chapter we begin with investigating the Pettis, Bochner, Gelfand, Dunford, McShane and Kurzweil- Henstock integrals in the context of Banach spaces, and give some comparison results.

Furthermore, we introduce the Pettis-Kurzweil-Henstock integral for Riesz space-valued functions, giving a Hake-type convergence theorem and a version of the Levi monotone convergence theorem.