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

DOI:
https://doi.org/10.1090/S0002-9939-1994-1174489-4

MathSciNet review:
1174489

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Abstract: We extend a nonsingular noninvertible map on to a minimal nonsingular automorphism containing as a factor and preserving some measure theoretic properties of . We call the automorphism the natural extension of . We compute some examples of natural extensions: first when is a shift with a product measure, and then generalize the result to some nonexact examples as well.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1994-1174489-4

Keywords:
Ergodic theory,
nonsingular endomorphisms

Article copyright:
© Copyright 1994
American Mathematical Society