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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Norbert Wiener's ergodic theorem for convex regions


Authors: Norberto A. Fava and Jorge H. Nanclares
Journal: Trans. Amer. Math. Soc. 235 (1978), 403-406
MSC: Primary 28A65
DOI: https://doi.org/10.1090/S0002-9947-1978-0463399-9
MathSciNet review: 0463399
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Abstract: It is proved that the geometric hypothesis of a theorem which generalizes Norbert Wiener's multiparameter ergodic theorem are satsified in the case of arbitrary convex regions, provided only that they form a substantial family as defined in the introduction.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1978-0463399-9
Keywords: Ergodic theorem, k-parameter semigroup, measure preserving transformations, convex compact sets, supporting hyperplanes, Blaschke's selection theorem
Article copyright: © Copyright 1978 American Mathematical Society