A weak law for normed weighted sums of random elements in Rademacher type \(p\) Banach spaces (Q1176230)

Let \(\{V_ n; n\geq 1\}\) be a sequence of r.v.s with values in a real separable, Rademacher type \(p\) (\(1\leq p\leq 2\)) Banach space and stochastically dominated by a r.v. \(V\). Let \(\{a_ n; n\geq 1\}\) and \(\{b_ n; n\geq 1\}\) be suitable constants satisfying growth conditions. A weak law of large numbers of the form \((\sum^ n_{j=1}a_ jV_ j- \nu_ n)/b_ n@>P>>0\) holds for some sequence \(\{\nu_ n; n\geq 1\}\) whenever \(nP\{\| DV\|>b_ n/| a|\}=O(1)\).