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