Weakly Orthogonally Additive Functionals on Mcshane-Bochner Integral Function Spaces Defined in Euclidean Spaces Rn

Abstract

The study of weakly orthogonal additive functions impacts the structural properties of a function space and allows further investigation into the solution of broader mathematical problems. The aim of this research is to analyze the properties and application of weak orthogonal additive functions on the McShane-Bochner integral function space defined in Euclidean space. . The research method used is Research and Development (R&D). This type of research is descriptive qualitative. Population in this study is Vectors in Euclidean Space RN\mathbb{R}^NRN: This research begins by conducting a preliminary analysis through literature study, then testing the theory, carrying out evaluations, and drawing conclusions. After that the theory that had been developed was tested through Focus Group Discussion activities. This research succeeded in building a function space which is a collection of McShane-Bochner integral functions defined in cells.  in Euclidean space  that meets certain characteristics. Based on this function space, the Representation Theorem for weakly orthogonal additive functions is then constructed in the newly constructed function space. The implication of this research is that this research enriches understanding of the structure and properties of McShane-Bochner integrable functions, which is an important generalization in functional analysis and integration theory.