The Annals of Probability

Records in a Partially Ordered Set

Charles M. Goldie and Sidney Resnick

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We consider independent identically distributed observations taking values in a general partially ordered set. Under no more than a necessary measurability condition we develop a theory of record values analogous to parts of the well-known theory of real records, and discuss its application to many partially ordered topological spaces. In the particular case of $\mathbb{R}^2$ under a componentwise partial order, assuming the underlying distribution of the observations to be in the domain of attraction of an extremal law, we give a criterion for there to be infinitely many records.

Article information

Ann. Probab., Volume 17, Number 2 (1989), 678-699.

First available in Project Euclid: 19 April 2007

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Zentralblatt MATH identifier


Primary: 60B05: Probability measures on topological spaces
Secondary: 60K99: None of the above, but in this section 06A10

Bivariate extremal law continuous lattice Fell topology hazard measure lattice Lawson topology partially ordered set random closed set records semicontinuity sup vague topology upper semicontinuity


Goldie, Charles M.; Resnick, Sidney. Records in a Partially Ordered Set. Ann. Probab. 17 (1989), no. 2, 678--699. doi:10.1214/aop/1176991421.

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