Computability of the Radon-Nikodym derivative

Mathieu Hoyrup 1 Cristobal Rojas 2 Klaus Weihrauch 3
1 CARTE - Theoretical adverse computations, and safety
Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
2 Department of Mathematics [University of Toronto]
3 Fakultät für Mathematik und Informatik [Hagen]
Abstract : We show that computability of the Radon-Nikodym derivative of a measure μ absolutely continuous w.r.t. some other measure λ can be reduced to a single application of the non-computable operator EC, which transforms enumeration of sets (in N) to their characteristic functions. We also give a condition on the two measures (in terms of the computability of the norm of a certain linear operator involving the two measures) which is sufficient to compute the derivative.
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Communication dans un congrès
Benedikt Löwe and Dag Normann and Ivan Soskov and Alexandra Soskova. Computability in Europe, Jun 2011, Sofia, Bulgaria. Springer-Verlag, 6735, pp.132-141, 2011, LNCS
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Mathieu Hoyrup, Cristobal Rojas, Klaus Weihrauch. Computability of the Radon-Nikodym derivative. Benedikt Löwe and Dag Normann and Ivan Soskov and Alexandra Soskova. Computability in Europe, Jun 2011, Sofia, Bulgaria. Springer-Verlag, 6735, pp.132-141, 2011, LNCS. 〈inria-00586740〉

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