Kurzweil-Henstock Integral in Riesz spaces

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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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Integration in Metric Semigroups

Pp. 198-212 (15)

Antonio Boccuto, Beloslav Riecan and Marta Vrabelova


In this chapter we present a Kurzweil-Henstock-type integral for metric semigroup-valued functions, defined on (possibly unbounded) subintervals of the extended real line. An example of a metric semigroup which is not a group is the set of all fuzzy numbers.

Besides the elementary properties we prove a version of the Henstock lemma and some convergence theorems in this setting.