## The Annals of Probability

### Records in a Partially Ordered Set

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176991421

Digital Object Identifier
doi:10.1214/aop/1176991421

Mathematical Reviews number (MathSciNet)
MR985384

Zentralblatt MATH identifier
0678.60001

JSTOR

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

#### Citation

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