2010/03/24 by N. H. Bingham, Ν. H. Bingham, Bingham, N. H. +2
Mathematics · #26A03 #Advanced Topology and Set Theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematical and Theoretical Analysis #Probability (math.PR) #math.CA #math.PR #msc:26A03
paper · pdf · doi:10.48550/arxiv.1003.4673
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
arxiv created 2010/03/24 · openalex publication_date 2010/03/24 · arxiv updated 2010/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Kingman's Theorem on skeleton limits---passing from limits as n→ ∞ along nh (n∈ ℕ) for enough h>0 to limits as t→ ∞ for t∈ 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.