A Formula for an Equivalent Invariant Measure

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jan 1985Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 93, page 32 (issn: 0002-9939,

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Authors: Maharam, Dorothy;

doi: 10.2307/2044547 , 10.1090/s0002-9939-1985-0766521-9

A Formula for an Equivalent Invariant Measure

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Abstract

Let T T be a nonsingular 1 − 1 1 - 1 measurable transformation of a finite measure space ( X , B , m ) (X,B,m) . A simple construction is given for a σ \sigma -finite measure μ \mu , equivalent to m m and invariant under T T , when such a measure exists.

Keywords

invariant measure, measurable transformation, Radon-Nikodým derivative, Ergodic theory, Measure-preserving transformations

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