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- W2047613963 abstract "Karamata theory (N.H. Bingham et al. (1987) [8, Ch. 1] ) explores functions f for which the limit function g ( λ ) : = f ( λ x ) / f ( x ) exists (as x → ∞ ) and for which g ( λ ) = λ ρ subject to mild regularity assumptions on f . Further Karamata theory (N.H. Bingham et al. (1987) [8, Ch. 2] ) explores functions f for which the upper limit f * ( λ ) : = lim sup f ( λ x ) / f ( x ) , as x → ∞ , remains bounded. Here the usual regularity assumptions invoke boundedness of f * on a Baire non-meagre/measurable non-null set, with f Baire/measurable, and the conclusions assert uniformity over compact λ -sets (implying upper bounds of the form f ( λ x ) / f ( x ) ⩽ K λ ρ for all large λ , x ). We give unifying combinatorial conditions which include the two classical cases, deriving them from a combinatorial semigroup theorem. We examine character degradation in the passage from f to f * (using some standard descriptive set theory) and thus identify natural classes in which the theory may be established." @default.
- W2047613963 created "2016-06-24" @default.
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- W2047613963 date "2010-10-01" @default.
- W2047613963 modified "2023-10-14" @default.
- W2047613963 title "Regular variation without limits" @default.
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- W2047613963 doi "https://doi.org/10.1016/j.jmaa.2010.04.013" @default.
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