Information-based complexity
Complexity theory of real functions
Complexity theory of real functions
The real number model in numerical analysis
Journal of Complexity
Theoretical Computer Science - Special issue on real numbers and computers
Computability on the probability measures on the Borel sets of the unit interval
Theoretical Computer Science - Special issue on computability and complexity in analysis
Complexity and information
Computable analysis: an introduction
Computable analysis: an introduction
Towards computability of elliptic boundary value problems in variational formulation
Journal of Complexity
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Traub and Werschulz [Complexity and Information, Cambridge University Press, New York, 1999] ask whether every linear operator S:@?X-Y is ''computable on the average'' w.r.t. a Gaussian measure on X. The question is inspired by an analogous result in information-based complexity on the average-case solvability of linear approximation problems. We give several interpretations of Traub and Werschulz' question within the framework of type-2 theory of effectivity. We have negative answers to all of these interpretations but the one with minimal requirements on the algorithm's uniformness. On our way to these results, we give an effective version of the Mourier-Prokhorov characterization of Gaussian measures on separable Hilbert spaces.