An ergodic theorem for Fréchet-valued random variables

Landers, D.; Rogge, L.

doi:10.1090/S0002-9939-1978-0501293-0

An ergodic theorem for Fréchet-valued random variables
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by D. Landers and L. Rogge PDF

Proc. Amer. Math. Soc. 72 (1978), 49-53 Request permission

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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