Integral of Ordered Banach Algebra Valued Measurable Functions

Wafa Y. Yahya; Noori F. Al-Mayahi

doi:10.24996/ijs.2024.65.2.16

Authors

Wafa Y. Yahya Mathematics Department, Education College, Al-Hamdaniya University, Mosul, Iraq https://orcid.org/0000-0001-9012-0134
Noori F. Al-Mayahi Mathematics Department, Science College, Al-Qadisiyah University, Al-Diwaniyah, Iraq

DOI:

https://doi.org/10.24996/ijs.2024.65.2.16

Keywords:

simple function, norm Banach algebra, absolute continuous, Integrable functions, ordered Banach algebra

Abstract

This research is concerned with the set of functions in ordered Banach algebra values that links up between functional analysis and measure theory. We generalized the concept of integration by using the measure space and the measurable function where is an ordered Banach algebra by using the integration of a simple measurable function with values in an ordered Banach algebra space (represented by an indicator function that has values in an ordered Banach algebra) and the integral of a non-negative measurable function that has values in an ordered Banach algebra. The aim of this research is to define the integration of functions by using the measure in the ordered Banach algebra space. This study generalized the definition of integration for the measurable function with values in the ordered Banach algebra space.