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

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