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Proceedings of the American Mathematical Society

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Sequential convergence to invariance in $ BC(G)$

Author: Robert Sine
Journal: Proc. Amer. Math. Soc. 55 (1976), 313-317
MSC: Primary 43A07; Secondary 28A65
MathSciNet review: 0412733
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Abstract: In this note it is shown that weak and strong convergence to invariance are equivalent for a sequence of probabilities acting on $ BC(G)$ of a noncompact locally compact group. This result was known for $ G = Z$. For other generalizations of the bounded sequences on $ Z$, say $ BUC(G)$, the result does not hold.

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Keywords: Convergence to invariance, Banach limits, means on groups, almost convergence
Article copyright: © Copyright 1976 American Mathematical Society

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