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Transactions of the American Mathematical Society

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A construction of uncountably many weak von Neumann transformations

Author: Karl David
Journal: Trans. Amer. Math. Soc. 257 (1980), 397-410
MSC: Primary 28D20
MathSciNet review: 552266
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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 [Enhancements On Off] (What's this?)

  • Nathaniel A. Friedman, Introduction to ergodic theory, Van Nostrand Reinhold Co., New York-Toronto, Ont.-London, 1970. Van Nostrand Reinhold Mathematical Studies, No. 29. MR 0435350
  • Paul Shields, Cutting and independent stacking of intervals, Math. Systems Theory 7 (1973), 1–4. MR 322138, DOI
  • Ya. G. Sinai, Weak isomorphism of transformations with invariant measure, Amer. Math. Soc. Transl. (2) 57 (1966), 123-143.

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Article copyright: © Copyright 1980 American Mathematical Society