EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 80(94), pp. 121–140 (2006)

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Henrik Hult and Filip Lindskog

Division of Applied Mathematics, Brown University, Providence, USA; and Department of Mathematics, KTH, Stockholm, Sweden

Abstract: The foundations of regular variation for Borel measures on a complete separable space $\mathbf S$, that is closed under multiplication by nonnegative real numbers, is reviewed. For such measures an appropriate notion of convergence is presented and the basic results such as a Portmanteau theorem, a mapping theorem and a characterization of relative compactness are derived. Regular variation is defined in this general setting and several statements that are equivalent to this definition are presented. This extends the notion of regular variation for Borel measures on the Euclidean space $\mathbf R^d$ to more general metric spaces. Some examples, including regular variation for Borel measures on $\mathbf R^d$, the space of continuous functions $\mathbf C$ and the Skorohod space $\mathbf D$, are provided.

Classification (MSC2000): 28A33

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Electronic fulltext finalized on: 10 Oct 2006. This page was last modified: 4 Dec 2006.

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© 2006 ELibM and FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition