Regular variation for measures on metric spaces

Henrik Hult, Filip Lindskog
2006 Publications de l'Institut Mathématique (Beograd)  
In this paper the foundations of regular variation for Borel measures on a complete separable space 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
more » ... his definition are presented. This extends the notion of regular variation for Borel measures on the Euclidean space R d to more general metric spaces. Some examples, including regular variation for Borel measures on R d , the space of continuous functions C and the Skorohod space D, are provided.
doi:10.2298/pim0694121h fatcat:hikwhp7uyjbcfhdgtatrxp6idq