Computable Riesz Representation for Locally Compact Hausdorff Spaces
Дата
Авторы
Lu,Hong
Weihrauch,Klaus
Journal Title
Journal ISSN
Volume Title
Издатель
Journal of Universal Computer Science
Аннотация
Описание
By the Riesz Representation Theorem for locally compact Hausdorff spaces, for every positive linear functional I on K(X) there is a measure μ such that I(f) =∫ f dμ where K(X) is the set of continuous real functions with compact support on the locally compact Hausdorff space X. In this article we prove a uniformly computable version of this theorem for computably locally compact computable Hausdorff 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 a measure μ can be computed and vice versa such that I(f) = ∫ f dμ.
Ключевые слова
computable analysis , computable topology , Hausdorff spaces , Riesz representation theorem