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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
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.

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

  • [1] H. G. Eggleston, Convexity, Cambridge University Press, New York, 1958. MR 23 #A2123. MR 0124813 (23:A2123)
  • [2] N. A. Fava, k-parameter semigroups of measure-preserving transformations, Trans. Amer. Math. Soc. 177 (1973), 345-352. MR 47 #6995. MR 0318448 (47:6995)
  • [3] N. Wiener, The ergodic theorem, Duke Math. J. 5 (1939), 1-18. MR 1546100

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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

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