$\sigma$-finite invariant measures on infinite product spaces
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- by David G. B. Hill
- Trans. Amer. Math. Soc. 153 (1971), 347-370
- DOI: https://doi.org/10.1090/S0002-9947-1971-0274725-1
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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.References
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Bibliographic Information
- © Copyright 1971 American Mathematical Society
- 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