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Transactions of the American Mathematical Society

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Amenable relations for endomorphisms

Author: J. M. Hawkins
Journal: Trans. Amer. Math. Soc. 343 (1994), 169-191
MSC: Primary 28D99
MathSciNet review: 1179396
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Abstract: We give necessary and sufficient conditions for an endomorphism to admit an equivalent invariant $ \sigma $-finite measure in terms of a generalized Perron-Frobenius operator. The assumptions are that the endomorphism is nonsingular (preserves sets of measure zero), conservative, and finite-to-1. We study two orbit equivalence relations associated to an endomorphism, and their connections to nonsingularity, ergodicity, and exactness. We also discuss Radon-Nikodym derivative cocycles for the relations and the endomorphism, and relate these to the Jacobian of the endomorphism.

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