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The strong asymptotic equivalence and the generalized inverse. (Russian, English) Zbl 1164.26303
Sib. Mat. Zh. 49, No. 4, 786-795 (2008); translation in Sib. Math. J. 49, No. 4, 628-636 (2008).
Summary: We discuss the relationship between the strong asymptotic equivalence relation and the generalized inverse in the class $$\mathcal A$$ of all nondecreasing and unbounded functions, defined and positive on a half-axis $$[a,+\infty)$$ ($$a > 0$$). In the main theorem, we prove a proper characterization of the function class $$IRV\cap\mathcal A$$, where $$IRV$$ is the class of all $$\mathcal O$$-regularly varying functions (in the sense of Karamata) having continuous index function.

##### MSC:
 26A12 Rate of growth of functions, orders of infinity, slowly varying functions
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