Resumen de Complete moment convergence for weighted sums of sequences of independent random elements in Banach spaces

Dehua Qiu, Henar Urmeneta Martín-Calero, Andrei Volodin

• In this paper, we obtain complete moment convergence results for weighted sums of sequences of independent random elements in a real separable Banach spaces without any geometric conditions imposed on the Banach space. Our results improve and extend some well known results from the literature. Furthermore, we obtain a complete moment convergence results for weighted sums of arrays of arbitrary random elements.