-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 | References | Similar Articles | Additional Information
Abstract: A necessary and sufficient condition in terms of Hellinger integrals is established for the existence of a -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
-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:
https://doi.org/10.1090/S0002-9947-1971-0274725-1
Keywords:
Invariant measures,
measures on infinite products,
Hellinger integrals,
Ornstein's transformation,
transformations wihout invariant measures,
-finite invariant measures
Article copyright:
© Copyright 1971
American Mathematical Society