Rapid variation with remainder and rates of convergence

(op voorblad per abuis E. Beirland vermeld, in plaats van J. Beirlant) The remainder term of the class \Gamma$ of rapidly varying fuctions Is considered. Some probabilistic applIcations to limit laws of extreme value theory and to the estlmation of the indexparameter of a regularly varying tail are considered. Keywords and Phrases: regular variation, rates of convergence, domains of attraction.