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)


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.


Measurable Space Single Application Computable Function Computable Element Computable Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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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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