Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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?)

  • [1] 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 (55 #8310)
  • [2] Paul Shields, Cutting and independent stacking of intervals, Math. Systems Theory 7 (1973), 1–4. MR 0322138 (48 #502)
  • [3] Ya. G. Sinai, Weak isomorphism of transformations with invariant measure, Amer. Math. Soc. Transl. (2) 57 (1966), 123-143.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 28D20

Retrieve articles in all journals with MSC: 28D20


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1980-0552266-7
PII: S 0002-9947(1980)0552266-7
Article copyright: © Copyright 1980 American Mathematical Society