Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 28D99

Retrieve articles in all journals with MSC: 28D99

Additional Information

Keywords: Construction of invariant measure, nonsingular transformation, $ \sigma $-finite invariant measure, finite measure space
Article copyright: © Copyright 1988 American Mathematical Society

American Mathematical Society