On mutual independence

Gary L. Wise and Eric B. Hall

Statistics & Probability Letters, 1993, vol. 17, issue 5, 395-398

Abstract: For any integer N > 1, we construct a probability space and N standard Gaussian random variables X1, X2,..., XN such that P(Xi [set membership, variant] Ai for each i [set membership, variant] I) = [Pi]i[set membership, variant]IP(Xi[set membership, variant]Ai) holds whenever the sets in {Ai: i [set membership, variant] I} are Borel sets but does not hold for all sets {Ai: i [set membership, variant] I} for which the indicated probabilities are well defined where I is any subset of {1, 2,..., N} having cardinality at least two. We then extend this result to the case where the random variables can have any diffuse distributions.

Keywords: Mutually; independent; mutually; Gaussian (search for similar items in EconPapers)
Date: 1993
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