Computable Riesz Representation for Locally Compact Hausdorff Spaces

Abstract: by the riesz representation theorem for locally compact hausdor. spaces, for every positive linear functional i on k(x) there is a measure μ such that i(f)= ∫ fdμ ,where k(x) is the set of continuous real functions with compact support on the locally compact hausdor. space x. in this article we prove a uniformly computable version of this theorem for computably locally compact computable hausdor. spaces x. we introduce a representation of the positive linear functionals i on k(x)and a representation of the borel measures on x and prove that for every such functional i ameasure μ can be computed and vice versa such that i(f)= ∫ fdμ