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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Author: Yoshihiro Kubokawa
Journal: Proc. Amer. Math. Soc. 102 (1988), 373-380
MSC: Primary 28D99
MathSciNet review: 921002
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0921002-7
PII: S 0002-9939(1988)0921002-7
Keywords: Construction of invariant measure, nonsingular transformation, $ \sigma $-finite invariant measure, finite measure space
Article copyright: © Copyright 1988 American Mathematical Society