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Displaying similar documents to “Sur les fonctions intégrables au sens de Lebesgue”

Sur la convergence en moyenne pour des vecteurs aléatoires intégrables au sens de Bochner

Luca Pratelli (1992)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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The problem of finding simple additional conditions, for a weakly convergent sequence in L 1 , which would suffice to imply strong convergence has been widely studied in recent years. In this Note we study this problem for Banach valued random vectors, by replacing weak convergence with a less restrictive assumption. Moreover, all the additional conditions we consider are also necessary for strong convergence, and they depend only on marginal distributions.