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Proceedings of the American Mathematical Society

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$ {\rm tan}\ x$ is ergodic


Author: F. Schweiger
Journal: Proc. Amer. Math. Soc. 71 (1978), 54-56
MSC: Primary 28A65; Secondary 10K99
MathSciNet review: 0473144
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Abstract: It is proved that the transformation $ x \mapsto \tan x$ is ergodic on the real line with respect to Lebesgue measure.


References [Enhancements On Off] (What's this?)

  • [1] J. H. B. Kemperman, The ergodic behavior of a class of real transformations, Stochastic Processes and Related Topics (Proc. Summer Res. Inst. on Statist. Inference for Stochastic Processes, Indiana Univ., Bloomington, Indiana, 1974), Academic Press, New York, 1975, pp. 249-258. MR 0372156 (51:8372)
  • [2] F. Schweiger, Some remarks on ergodicity and invariant measures, Michigan Math. J. 22 (1975), 181-187. MR 0376590 (51:12765)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0473144-4
Keywords: Ergodicity, transformations of the real line into itself, dynamical systems
Article copyright: © Copyright 1978 American Mathematical Society