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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 aredoi:10.2298/pim0694121h fatcat:hikwhp7uyjbcfhdgtatrxp6idq