✦ LIBER ✦

On Probabilities of Linear Sets

✍ Scribed by W. Bryc; W. Smolenski

Publisher: Elsevier Science
Year: 1993
Tongue: English
Weight: 237 KB
Volume: 45
Category: Article
ISSN: 0047-259X
DOI: 10.1006/jmva.1993.1024

No coin nor oath required. For personal study only.

✦ Synopsis

If (\left(X_{k}\right){k=1}^{x}) is a sequence of independent random variables with probabilities of atoms bounded away from one and (E) is a Borel linear subspace of (\mathbb{R}^{x}), then the event (\left{\left(X{k}\right){k=1}^{X} \in E\right}) is a.s. equivalent to the event (\left{\left(X{k}\right)_{k=1}^{n} \in F\right}), where (F) is an affine subspace of (\mathbb{R}^{n}) for some (n \geqslant 1). 1993 Academic Press. Inc.

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