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