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.
"Limit Properties of Random Variables Associated with a Partial Ordering of $R^d$." Ann. Probab. 5 (3) 395 - 403, June, 1977. https://doi.org/10.1214/aop/1176995800