Steele, J Michael2023-05-232023-05-2319772017-08-24https://repository.upenn.edu/handle/20.500.14332/47560A limit theorem is established for the length of the longest chain of random values in Rd 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.The original and published work is available at: https://projecteuclid.org/euclid.aop/1176995800#abstractmonotone subsequenceslower layerspartial orderingdiscrepancy functionssubadditive processesPhysical Sciences and MathematicsArticle