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.
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