Sequential Regular Variation: Extensions of Kendall’s Theorem

Source abstract

Abstract Regular variation is a continuous-parameter theory; we work in a general setting, containing the existing Karamata, Bojanic–Karamata/de Haan and Beurling theories as special cases. We give sequential versions of the main theorems, that is, with sequential rather than continuous limits. This extends the main result, a theorem of Kendall’s (which builds on earlier work of Kingman and Croft), to the general setting.