On the Exactness of the Lévy-Transformation

  • Vilmos Prokaj
Part of the Lecture Notes in Mathematics book series (LNM, volume 2123)


In a recent paper we gave a sufficient condition for the strong mixing property of the Lévy-transformation. In this note we show that it actually implies a much stronger property, namely exactness.


Continuous Function Stochastic Process Probability Measure Probability Theory Measurable Function 
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The author thanks Michel Emery for reading the first version of this note and offering helpful comments, and the referee for suggesting a simplification in the proof of Proposition 3.


  1. 1.
    V. Prokaj, Some Sufficient Conditions for the Ergodicity of the Lévy-Transformation, ed. by C. Donati-Martin, A. Lejay, A. Rouault. Séminaire de Probabilités, XLV (Springer, New York, 2013), pp. 93–121. Doi: 10.1007/978-3-319-00321-4_2, arxiv:1206.2485Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of Probability Theory and StatisticsEötvös Loránd UniversityBudapestHungary

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