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

Suchanek, Ana Mari­a

Journal of Multivariate Analysis, 1978, vol. 8, issue 4, 589-597

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

Date: 1978
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