
Journal of Convex Analysis 28 (2021), No. 1, 197202 Copyright Heldermann Verlag 2021 PermutationInvariance in Komlós' Theorem for HilbertSpace Valued Random Variables Abdessamad Dehaj Laboratory of Algebra, Analysis and Applications, Department of Mathematics and Computer Science, Faculty of Sciences Ben M'Sik, Hassan II University, Sidi Othman  Casablanca, Morocco a.dehaj@gmail.com Mohamed Guessous Laboratory of Algebra, Analysis and Applications, Department of Mathematics and Computer Science, Faculty of Sciences Ben M'Sik, Hassan II University, Sidi Othman  Casablanca, Morocco guessousjssous@yahoo.fr [Abstractpdf] The Koml\'{o}s theorem states that we can extract a subsequence from every $L_{\mathbb{R}}^{1}$bounded sequence of random variables, so that every further subsequence converges Ces\`{a}ro a.e. to the same limit. The purpose of this paper is to prove that if $\mathbb{H}$ is a Hilbert space, we can extract a subsequence from every $L_{\mathbb{H}}^{1}$bounded sequence, so that every permuted subsequence converges Ces\`{a}ro a.e. in $\mathbb{H}$ to the same limit. Keywords: Bounded sequences, Cesaroconvergence, Hilbert space, Komlos theorem, permutation. MSC: 28A20, 46B20. [ Fulltextpdf (91 KB)] for subscribers only. 