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)



On continuity of invariant measures

Author: Andrew Adler
Journal: Proc. Amer. Math. Soc. 41 (1973), 487-491
MSC: Primary 28A70; Secondary 43A07
MathSciNet review: 0328025
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Main Theorem. Let $ \Phi $ be a set of transformations on a set $ X$. The following conditions are then equivalent:

(1) There is a noncontinuous finitely additive measure defined on all subsets of $ X$ and invariant under all transformations in $ \Phi $.

(2) There is an integer $ m$ such that for any finite subset $ F$ of $ \Phi $ there is a finite subset $ {A_F}$ of $ X$, with no more than $ m$ elements, such that each $ f$ in $ F$ acts as a permutation on $ {A_F}$.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 28A70, 43A07

Retrieve articles in all journals with MSC: 28A70, 43A07

Additional Information

Keywords: Finitely additive, invariant, measure, continuous, ultrafilter
Article copyright: © Copyright 1973 American Mathematical Society

American Mathematical Society