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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Examples of natural extensions of nonsingular endomorphisms


Authors: K. G. Dajani and J. M. Hawkins
Journal: Proc. Amer. Math. Soc. 120 (1994), 1211-1217
MSC: Primary 28D99
MathSciNet review: 1174489
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Abstract: We extend a nonsingular noninvertible map $ T$ on $ (X,\mathcal{B},\mu )$ to a minimal nonsingular automorphism containing $ T$ as a factor and preserving some measure theoretic properties of $ T$. We call the automorphism the natural extension of $ T$. We compute some examples of natural extensions: first when $ T$ is a shift with $ \mu $ a product measure, and then generalize the result to some nonexact examples as well.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1174489-4
PII: S 0002-9939(1994)1174489-4
Keywords: Ergodic theory, nonsingular endomorphisms
Article copyright: © Copyright 1994 American Mathematical Society