Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Complexity theory of real functions
Complexity theory of real functions
Computable analysis: an introduction
Computable analysis: an introduction
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 the dual of C[0;1], for every continuous linear operator F:C[0;1]-R there is a function g:[0;1]-R of bounded variation such thatF(f)=@!fdg(f@?C[0;1]). The function g can be normalized such that V(g)=@?F@?. In this paper we prove a computable version of this theorem. We use the framework of TTE, the representation approach to computable analysis, which allows to define natural computability for a variety of operators. We show that there are a computable operator S mapping g and an upper bound of its variation to F and a computable operator S^' mapping F and its norm to some appropriate g.