Constructive Equivalence Relations on Computable Probability Measures

  • Laurent Bienvenu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3967)


We study the equivalence relations on probability measures corresponding respectively to having the same Martin-Löf random reals, having the same Kolmogorov-Loveland random reals, and having the same computably random reals. In particular, we show that, when restricted to the class of strongly positive generalized Bernoulli measures, they all coincide with the classical equivalence, which requires that two measures have the same nullsets.


Computable Strategy Computable Function Uniform Measure Random Real Computable Measure 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Laurent Bienvenu
    • 1
  1. 1.Laboratoire d’Informatique FondamentaleMarseilleFrance

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