Constructive equivalence relations on computable probability measures

Authors:
Laurent Bienvenu
Affiliations:
Laboratoire d'Informatique Fondamentale, Marseille, France
Venue:
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
Year:
2006

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Abstract

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.