ON THE CONVERGENCE THEOREMS OF THE McSHANE INTEGRAL FOR RIESZ-SPACES-VALUED FUNCTIONS DEFINED ON REAL LINE

Abstract

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