A construction of finite and 𝜎-finite invariant measures in measure spaces

Kubokawa, Yoshihiro

doi:10.1090/S0002-9939-1988-0921002-7

A construction of finite and $\sigma$-finite invariant measures in measure spaces
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by Yoshihiro Kubokawa

Proc. Amer. Math. Soc. 102 (1988), 373-380

DOI: https://doi.org/10.1090/S0002-9939-1988-0921002-7

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Abstract:

Let $T$ be a bijective nonsingular transformation on a finite measure space. We shall first construct a $\sigma$-finite and finite invariant measure by a unified method which is valid for both cases. Secondly we shall give another construction of a finite invariant measure. We shall also give a new necessary and sufficient condition of a unified form for the existence of $\sigma$-finite and finite invariant measures. Further, we shall discuss in detail ergodic transformations.

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