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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

$ \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
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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1971-0274725-1
PII: S 0002-9947(1971)0274725-1
Keywords: Invariant measures, measures on infinite products, Hellinger integrals, Ornstein's transformation, transformations wihout invariant measures, $ \sigma $-finite invariant measures
Article copyright: © Copyright 1971 American Mathematical Society