| Abstract: | A generalization of regular variation is discussed. The property 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 doing so 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. |
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