We obtain weighted strong law of large numbers for a sequence of random variables belonging to variable exponent vector-valued Lebesgue spaces. As an application, we establish sufficient conditions for the convergence of weighted ergodic averages and weighted series of contractions in Banach spaces.
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Farrukh Mukhamedov, Humberto Rafeiro, Weighted strong laws of large numbers on variable exponent vector-valued Lebesgue spaces. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 31 (2020), no. 4, pp. 791–814DOI 10.4171/RLM/915