DOI: 10.68381/jca28014 ISSN: 0944-6532
Permutation-Invariance in Komlós' Theorem for Hilbert-Space Valued Random Variables
Abdessamad Dehaj, Mohamed Guessous
The Komlós theorem states that we can extract a subsequence from every
L_{\mathbb{R}}^{1}
L
R
1
-bounded sequence of random variables, so that every further subsequence converges Cesàro a.e. to the same limit. The purpose of this paper is to prove that if
\mathbb{H}
H
is a Hilbert space, we can extract a subsequence from every
L_{\mathbb{H}}^{1}
L
H
1
-bounded sequence, so that every permuted subsequence converges Cesàro a.e. in
\mathbb{H}
H
to the same limit.