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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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Keywords: Ergodic theory, nonsingular endomorphisms
Article copyright: © Copyright 1994 American Mathematical Society

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