Abstract
We study the problem of the existence of a true exceptional set for an asymptotic formula, that is a minimal set --- up to finite modifications --- such that the asymptotic formula holds outside such a set. We give an analytic and a descriptive set theoretic characterisations for the existence of a true exceptional set, which we then apply by showing the non-existence of a true exceptional set in some well known situations. We prove in fact that, both from a category and a measure theoretic points of view, most asymptotic formulas do not have a true exceptional set.
Citation
Danilo Bazzanella. Riccardo Camerlo. "The class of the exceptional sets for a general asymptotic formula." Funct. Approx. Comment. Math. 51 (2) 347 - 362, December 2014. https://doi.org/10.7169/facm/2014.51.2.7
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