Let A be an ordered algebra and E be a Banach lattice. We let L(E) denote the vector space of bounded linear operators on E. A positive representation of A on E is an algebra homomorphism ?:A?L(E) such that ?(A_ amp;#??; )?L_r (E)_ amp;#??;. In this thesis, we introduce the bounded positive representation on non-empty set X and positive spectral measure on arbitrary ?-algebra. At the end, we study the relationship between the positive representation of C_? (X) on the Banach lattice E and study the spectral measure on the Borel ?-algebra B(X) of X, in which X is a locally compact Hausdorff space. Then we examine the condition of a generating regular positive spectral measure for positive representations.