Cline, Daren B. H. Intermediate regular and \(\Pi\) variation. (English) Zbl 0793.26004 Proc. Lond. Math. Soc., III. Ser. 68, No. 3, 594-616 (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 \(\Pi\)-variation, a generalization of \(\Pi\)-variation. Paralleling the theories of regular and \(\Pi\)-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. Reviewer: D.B.H.Cline (College Station) Cited in 43 Documents MSC: 26A12 Rate of growth of functions, orders of infinity, slowly varying functions 26A48 Monotonic functions, generalizations 40E05 Tauberian theorems 60F05 Central limit and other weak theorems Keywords:\(\Pi\)-variation; Karamata theorem; Tauberian theorem; intermediate regular variation PDFBibTeX XMLCite \textit{D. B. H. Cline}, Proc. Lond. Math. Soc. (3) 68, No. 3, 594--616 (1994; Zbl 0793.26004) Full Text: DOI