The Riesz Representation Operator on the Dual of C[0; 1] is Computable

By the riesz representation theorem, for every linear functional f : c[0; 1] → r there is a function g : [0; 1] → r of bounded variation such that f(h) =∫ h dg (h ∈ c[0; 1]) . a computable version is proved in [lu and weihrauch(2007)]: a function g can be computed from f and its norm, and f can be computed from g and an upper bound of its total variation. in this article we present a much more transparent proof. we first give a new proof of the classical theorem from which we then can derive the computable version easily. as in [lu and weihrauch(2007)] we use the framework of tte, the representation approach for computable analysis, which allows to define natural concepts of computability for the operators under consideration.