Geodesic
Permutation-Invariance in Komlós' Theorem for Hilbert-Space Valued Random Variables
Journal of convex analysis, Tome 28 (2021) no. 1, pp. 197-202
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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.
Classification : 28A20, 46B20
Mots-clés : Bounded sequences, Cesaro-convergence, Hilbert space, Komlos theorem, permutation 
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     author = {A. Dehaj and M. Guessous},
     title = {Permutation-Invariance in {Koml\'os'} {Theorem} for {Hilbert-Space} {Valued} {Random} {Variables}},
     journal = {Journal of convex analysis},
     pages = {197--202},
     year = {2021},
     volume = {28},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2021_28_1_JCA_2021_28_1_a13/}
}
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A. Dehaj; M. Guessous. Permutation-Invariance in Komlós' Theorem for Hilbert-Space Valued Random Variables. Journal of convex analysis, Tome 28 (2021) no. 1, pp. 197-202. http://geodesic.mathdoc.fr/item/JCA_2021_28_1_JCA_2021_28_1_a13/