Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Computability on random variables
Theoretical Computer Science - Special issue on computability and complexity in analysis
Computability on the probability measures on the Borel sets of the unit interval
Theoretical Computer Science - Special issue on computability and complexity in analysis
Computable analysis: an introduction
Computable analysis: an introduction
Theoretical Computer Science
A computable version of the Daniell-Stone theorem on integration and linear functionals
Theoretical Computer Science
Representing probability measures using probabilistic processes
Journal of Complexity
Towards computability of elliptic boundary value problems in variational formulation
Journal of Complexity
Computability on subsets of locally compact spaces
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
A computable version of dini's theorem for topological spaces
ISCIS'05 Proceedings of the 20th international conference on Computer and Information Sciences
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By the Riesz Representation Theorem for locally compact Hausdorff spaces, for every positive linear functional I on K(X) there is a measure @m such that I(f)=@!fd@m, 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 @m can be computed and vice versa such that I(f)=@!fd@m.