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On almost sure convergence of Cesaro averages of subsequences of vector-valued functions

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  • Suchanek, Ana Mari­a

Abstract

A remarkable theorem proved by Komlòs [4] states that if {fn} is a bounded sequence in L1(R), then there exists a subsequence {fnk} and f [set membership, variant] L1(R) such that fnk (as well as any further subsequence) converges Cesaro to f almost everywhere. A similar theorem due to Révész [6] states that if {fn} is a bounded sequence in L2(R), then there is a subsequence {fnk} and f [set membership, variant] L2(R) such that [Sigma]k=1[infinity] ak(fnk - f) converges a.e. whenever [Sigma]k=1[infinity] ak 2

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  • Suchanek, Ana Mari­a, 1978. "On almost sure convergence of Cesaro averages of subsequences of vector-valued functions," Journal of Multivariate Analysis, Elsevier, vol. 8(4), pages 589-597, December.
    • Handle: RePEc:eee:jmvana:v:8:y:1978:i:4:p:589-597
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    Cited by:

    1. Wang, Xaingchen & Bhaskara Rao, M. & Li, Deli, 1995. "Some results on strong limit theorems for (LB)-space-valued random variables," Statistics & Probability Letters, Elsevier, vol. 23(3), pages 247-251, May.

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