On Probabilities of Linear Sets

W. Bryc and W. Smolenski

Journal of Multivariate Analysis, 1993, vol. 45, issue 1, 25-33

Abstract: If (Xk)[infinity]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 [infinity], then the event {(Xk)[infinity]k = 1 [set membership, variant] E} is a.s. equivalent to the event {(Xk)nk = 1 [set membership, variant] F}, where F is an affine subspace of n for some n >= 1.

Date: 1993
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