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April, 1989 Records in a Partially Ordered Set
Charles M. Goldie, Sidney Resnick
Ann. Probab. 17(2): 678-699 (April, 1989). DOI: 10.1214/aop/1176991421


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.


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Charles M. Goldie. Sidney Resnick. "Records in a Partially Ordered Set." Ann. Probab. 17 (2) 678 - 699, April, 1989.


Published: April, 1989
First available in Project Euclid: 19 April 2007

zbMATH: 0678.60001
MathSciNet: MR985384
Digital Object Identifier: 10.1214/aop/1176991421

Primary: 60B05
Secondary: 06A10 , 60K99

Keywords: 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

Rights: Copyright © 1989 Institute of Mathematical Statistics


Vol.17 • No. 2 • April, 1989
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