Academic Editor: Youssef EL FOUTAYENI
Received |
Accepted |
Published |
30 January 2020 |
14 February 2020 |
10 March 2020 |
Abstract: Let (Ω, T, μ) be a finite measure space, X a Banach space and L1(, X) the Banach space of all equivalence classes of Bochner integrable functions. A well-Known result of Komlós’ [6] says the following: Every bounded sequence (fn)n of L1(, ) has a subsequence (fm)m such that its means of Césaro convergence almost everywhere to a real integrable function, moreover this convergence takes place for any subsequence of (fm)m. Several extensions of Komlós’ theorem to infinite dimensions has been given for exemple [1],[4],[5]. We aim to give a weak version of Komlós’ theorem for bounded sequences in L1(, X) related to the convergence of truncated functions.
