ON THE CONVERGENCE THEOREMS OF THE McSHANE INTEGRAL FOR RIESZ-SPACES-VALUED FUNCTIONS DEFINED ON REAL LINE - Ansori, Muslim; Sumanto, Yosephus D.; Dewi, Novi Rustiana (PYTHAGORAS Jurnal Matematika dan Pendidikan Matematika, 2007)
This paper is a partial result of our researchs in the main topic "On The McShane Integral for Riesz-Spaces-valued Functions Defined on the space ". We have constructed McShane integral for Riesz-spaces-valued functions defined on the space by a technique involving double sequences and proved some basic properties which coincides with the McShane Integral for Banach-spaces valued functions defined on real line. Further, we construct some convergence theorems involving uniformly convergence theorems, monotone convergence theorems and Fatou’s lemma in the sense of this integral.Keywords : Riesz Space, McShane Integral