On Probabilities of Linear Sets

If (Xk)∞k = 1 is a sequence of independent random variables with probabilities of atoms bounded away from one and E is a Borel linear subspace of R∞, then the event {(Xk)∞k = 1 ∈ E} is a.s. equivalent to the event {(Xk)nk = 1 ∈ F}, where F is an affine subspace of Rn for some n ≥ 1.