Intermediate Regular and Π Variation
Daren B. H. Cline · Proceedings of the London Mathematical Society · 1994
A generalization of regular variation is discussed which is intermediate to extended regular variation and O-regular variation. Analogous to this intermediate regular variation is intermediate Π-variation, a generalization of Π-variation. Paralleling the theories of regular variation and Π-variation, we demonstrate uniform convergence and representation theorems. We also prove a Karamata theorem and a Tauberian theorem for intermediate regular variation and in so doing we include an interesting extension to the corresponding results for O-regular variation. Contained in our proofs is the resolution of a measurability problem extant in other discussions of generalized regular variation.