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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



An ergodic theorem for Fréchet-valued random variables

Authors: D. Landers and L. Rogge
Journal: Proc. Amer. Math. Soc. 72 (1978), 49-53
MSC: Primary 60F15; Secondary 28A65
MathSciNet review: 0501293
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Abstract: We generalize the classical ergodic theorem from real-valued random variables to Fréchet space-valued random variables and obtain this generalization as a direct corollary of the classical theorem. As an application we obtain several strong laws of large numbers for Fréchet-valued random variables. In a similar way we obtain a martingale theorem for Fréchet-valued random variables.

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Keywords: Pointwise ergodic theorem, strong law of large numbers, weakly orthogonal processes
Article copyright: © Copyright 1978 American Mathematical Society