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Computability of the Radon-Nikodym derivative

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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https://hal.inria.fr/inria-00586740
Contributor : Mathieu Hoyrup <>
Submitted on : Monday, April 18, 2011 - 12:20:11 PM
Last modification on : Thursday, July 22, 2021 - 3:10:02 PM
Long-term archiving on: : Thursday, November 8, 2012 - 4:41:20 PM

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Mathieu Hoyrup, Cristobal Rojas, Klaus Weihrauch. Computability of the Radon-Nikodym derivative. Computability in Europe, Jun 2011, Sofia, Bulgaria. pp.132-141. ⟨inria-00586740⟩

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