  We develop a framework for regularly varying measures on complete separable
metric spaces $\mathbb{S}$ with a closed cone $\mathbb{C}$ removed, extending
material in Hult & Lindskog (2006), Das, Mitra & Resnick (2013). Our framework
provides a flexible way to consider hidden regular variation and allows
simultaneous regular variation properties to exist at different scales and
provides potential for more accurate estimation of probabilities of risk
regions. We apply our framework to iid random variables in
$\mathbb{R}_+^\infty$ with marginal distributions having regularly varying
tails and to c\`adl\`ag L\'evy processes whose L\'evy measures have regularly
varying tails. In both cases, an infinite number of regular variation
properties coexist distinguished by different scaling functions and state
spaces.
