On Kolmogorov SLLN Under Rearrangements for "Orthogonal" Random Variables in a B-Space

It is well-known that the Kolmogorov SLLN (non-i.i.d. case) fails for pair-wise independent random variables. However, as shown in the paper it can be saved even for orthogonal random variables if one allows permutations. We prove it in the setup of Banach space valued random variables.