Kingman, category and combinatorics

Abstract

Kingman's Theorem on skeleton limits---passing from limits as $n\to \infty$ along $nh$ ($n\in \mathbb{N}$) for enough $h>0$ to limits as $t\to \infty$ for $t\in \mathbb{R}$---is generalized to a Baire/measurable setting via a topological approach. We explore its affinity with a combinatorial theorem due to Kestelman and to Borwein and Ditor, and another due to Bergelson, Hindman and Weiss. As applications, a theory of `rational' skeletons akin to Kingman's integer skeletons, and more appropriate to a measurable setting, is developed, and two combinatorial results in the spirit of van der Waerden's celebrated theorem on arithmetic progressions are given.

34 pages. To appear in Bingham, N. H., and Goldie, C. M. (eds), Probability and Mathematical Genetics: Papers in Honour of Sir John Kingman. London Math. Soc. Lecture Note Series. Cambridge: Cambridge Univ. Press

Cited by in corpus (1)

• Uniformity and self-neglecting functions