Some results on the span of families of Banach valued independent, random variables - Rohan Hemasinha (International Journal of Mathematics and Mathematical Sciences)
Let E be a Banach space, and let (Ω,ℱ,P) be a probability space. If L1(Ω) contains an isomorphic copy of L1[0,1] then in LEP(Ω)(1≤P<∞), the closed linear span of every sequence of independent, E valued mean zero random variables has infinite codimension. If E is reflexive or B-convex and 1<P<∞ then the closed (in LEP(Ω)) linear span of any family of independent, E valued, mean zero random variables is super-reflexive.