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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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A construction of uncountably many weak von Neumann transformations
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by Karl David PDF
Trans. Amer. Math. Soc. 257 (1980), 397-410 Request permission

Abstract:

We define weak von Neumann transformations and discuss some of their properties, using several examples of countable classes of these transformations. Then we construct an uncountable class by the cutting-and-stacking method. We show that each member of this class is ergodic and has zero entropy.
References
  • Nathaniel A. Friedman, Introduction to ergodic theory, Van Nostrand Reinhold Mathematical Studies, No. 29, Van Nostrand Reinhold Co., New York-Toronto, Ont.-London, 1970. MR 0435350
  • Paul Shields, Cutting and independent stacking of intervals, Math. Systems Theory 7 (1973), 1–4. MR 322138, DOI 10.1007/BF01824799
  • Ya. G. Sinai, Weak isomorphism of transformations with invariant measure, Amer. Math. Soc. Transl. (2) 57 (1966), 123-143.
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 257 (1980), 397-410
  • MSC: Primary 28D20
  • DOI: https://doi.org/10.1090/S0002-9947-1980-0552266-7
  • MathSciNet review: 552266