Computability of the Radon-Nikodym Derivative

  • Mathieu Hoyrup
  • Cristóbal Rojas
  • Klaus Weihrauch
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6735)

Abstract

We show that a single application of the non-computable 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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Mathieu Hoyrup
    • 1
  • Cristóbal Rojas
    • 2
  • Klaus Weihrauch
    • 3
  1. 1.LORIA, INRIA Nancy-Grand EstVandoeuvre-lés-NancyFrance
  2. 2.Department of MathematicsUniversity of TorontoTorontoCanada
  3. 3.Fakultät für Mathematik und InformatikFernUniversität HagenHagenGermany

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