𝜎-finite invariant measures on infinite product spaces

Hill, David G. B.

doi:10.1090/S0002-9947-1971-0274725-1

$\sigma$ -finite invariant measures on infinite product spaces

Author: David G. B. Hill
Journal: Trans. Amer. Math. Soc. 153 (1971), 347-370
MSC: Primary 28.75
DOI: https://doi.org/10.1090/S0002-9947-1971-0274725-1
MathSciNet review: 0274725
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Abstract: A necessary and sufficient condition in terms of Hellinger integrals is established for the existence of a $\sigma$ -finite invariant measure on an infinite product space. Using this it is possible to construct a wide class of transformations on the unit interval which have no $\sigma$ -finite invariant measure equivalent to Lebesgue measure. This class includes most of the previously known examples of such transformations.

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