Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
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
A computable version of the Daniell-Stone theorem on integration and linear functionals
Theoretical Computer Science
Uniform test of algorithmic randomness over a general space
Theoretical Computer Science
Representing probability measures using probabilistic processes
Journal of Complexity
A constructive Borel-Cantelli lemma. Constructing orbits with required statistical properties
Theoretical Computer Science
Computability of probability measures and Martin-Löf randomness over metric spaces
Information and Computation
On the computational content of the brouwer fixed point theorem
CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
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We show that a single application of the noncomputable operator EC, which transforms enumerations of sets (in N) to their characteristic functions, suffices to compute the Radon-Nikodym derivative dµ/dλ of a finite measure µ, which is absolutely continuous w.r.t. the σ-finite measure λ. We also give a condition on the two measures (in terms of computability of the norm of a certain linear operator involving the two measures) which is sufficient to compute the derivative.