NDLI: Conditional Zero-One Laws

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Hess, K. T.
Copyright Year	2004
Abstract	We say that a class of events fulfills a conditional zero-one law if it is a subset of the completion of the conditioning $\sigma$-algebra. In this case the conditional probability of an event of the class is an indicator function. Therefore the conditional probability takes almost surely only the values zero and one; in the unconditional case the indicator functions are almost surely constant.We consider two special zero-one laws. If a sequence of random variables is conditionally independent, then its tail $\sigma$-algebra fulfills a conditional zero-one law; this generalizes Kolmogorov's zero-one law. If the sequence is even conditionally identically distributed, then its permutable $\sigma$-algebra, which contains the tail $\sigma$-algebra, fulfills a conditional zero-one law; this generalizes the zero-one law of Hewitt and Savage.
Starting Page	711
Ending Page	718
Page Count	8
File Format	PDF
ISSN	0040585X
DOI	10.1137/S0040585X97980804
e-ISSN	10957219
Journal	Theory of Probability & Its Applications (TPRBAU)
Issue Number	4
Volume Number	48
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-25
Access Restriction	Subscribed
Subject Keyword	conditional independence zero-one law conditional probability
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Statistics, Probability and Uncertainty

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Conditional Zero-One Laws