Limit Properties of Random Variables Associated with a Partial Ordering of $R^d$
John M. Steele · The Annals of Probability · 1977
A limit theorem is established for the length of the longest chain of random values in $R^d$ with respect to a partial ordering. The result is applied to a question raised by T. Robertson and F. T. Wright concerning the generalized empirical distribution function associated with the class of lower layers.