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
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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.

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