A probability inequality for sums of independent Banach space valued random variables. Issue 2 (17th February 2018) - Li, Deli; Liang, Han-Ying; Rosalsky, Andrew
Abstract : Let be a real separable Banach space. Let and be two continuous and increasing functions defined on such that, , and is a nondecreasing function on . Let be a sequence of independent and symmetricB -valued random variables. In this note, we establish a probability inequality for sums of independentB -valued random variables by showing that for every and all, where and, . As an application of this inequality, we establish what we call a comparison theorem for the weak law of large numbers for independent and identically distributed -valued random variables.