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Refinement of a zero-one law for maxima

✍ Scribed by R.J. Tomkins

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
27 KB
Volume
32
Category
Article
ISSN
0167-7152

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✦ Synopsis

The second part of Theorem 2 of this paper is a special case of Theorem 1 of Rothmann and Russo (Statistics & Probability Letters 11 (1991) 403-410). While the first part of Theorem 2 does not follow explicitly from Theorem 1 of Rothmann and Russo, it can be derived using the arguments in their proof. Even though Rothmann and Russo's result is stated for an i.i.d, sequence uniformly distributed on (0, 1), the pointwise argument used in their proof is applicable to any sequence of random variables bounded above by 1. A standard transformation argument then leads to the first part of Tomkins's Theorem 2.

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