# Sequential regular variation: extensions of Kendall's theorem

## TL;DR

This paper extends Kendall's theorem on regular variation to a more general setting using sequential limits, unifying several existing theories in the process.

## Contribution

It introduces sequential versions of key theorems in regular variation, broadening the scope of Kendall's theorem to a general framework.

## Key findings

- Unified existing regular variation theories
- Developed sequential limit versions of main theorems
- Extended Kendall's theorem to a general setting

## 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.