Publications de l'Institut Mathématique, Nouvelle SérieVol. 80(94), pp. 121–140 (2006)
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Publications de l'Institut Mathématique, Nouvelle Série Vol. 80(94), pp. 121–140 (2006) |
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REGULAR VARIATION FOR MEASURES ON METRIC SPACESHenrik Hult and Filip LindskogDivision of Applied Mathematics, Brown University, Providence, USA; and Department of Mathematics, KTH, Stockholm, SwedenAbstract: 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 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 10 Oct 2006. This page was last modified: 4 Dec 2006.
© 2006 Mathematical Institute of the Serbian Academy of Science and Arts
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