2016-06-032016-06-031997Ordóñez Cabrera, M.H. (1997). Convergence in mean of weighted sums of {an,k}-compactly uniformly integrable random elements in Banach spaces. International Journal of Mathematics and Mathematical Sciences, 20, 443-450.0161-17121687-0425http://hdl.handle.net/11441/41844The convergence in mean of a weighted sum ka.k(Xk EXk) of random elements in a separable Banach space is studied under a new hypothesis which relates the random elements with their respective weights in the sum: the {a.. }-compactly uniform integrability of {X. }. This condition, which is implied by the tightness of {X,,} and the {a,,k }-uniform integrability of {[IX,, II}, is weaker than the compactly miform integrability of {X,,} and leads to a result of convergence in mean which is strictly stronger than a recent result of Wang, Rao and Deli.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Weighted sumsrandom elements in separable Banach spacescompactly uniform integrability{an,k}-compactly uniform integrabilitytightness{an,k}- uniform integrabilityconvergence in meaninfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess10.1155/S0161171297000604https://idus.us.es/xmlui/handle/11441/41844