Integral of Ordered Banach Algebra Valued Measurable Functions

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.