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Invariant measures for general induced maps and towers

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  • Absolutely continuous invariant measures (acims) for general induced transformations are shown to be related, in a natural way, to popular tower constructions regardless of any particulars of the latter. When combined with (an appropriate generalization of) the known integrability criterion for the existence of such acims, this leads to necessary and sufficient conditions under which acims can be lifted to, or projected from, nonsingular extensions.
    Mathematics Subject Classification: Primary: 28D05, 37A40, 37C40.


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