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Intermediate regular and $$\Pi$$ variation. (English) Zbl 0793.26004
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.

##### MSC:
 26A12 Rate of growth of functions, orders of infinity, slowly varying functions 26A48 Monotonic functions, generalizations 40E05 Tauberian theorems, general 60F05 Central limit and other weak theorems
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