Tail measures and regular variation

A general framework for the study of regular variation (RV) is that Polish star-shaped metric spaces, while recent developments in [41] have discussed RV with respect to a properly localised boundedness B. Along lines latter approach, we discuss Borel measures and random processes on spaces (D,dD). Tail introduced [47] appear naturally as limiting regularly varying time series. We define tail measurable space (D,D) indexed by H(D), countable family 1-homogeneous coordinate maps, show some tractable instances investigation when B determined H(D). This allows us càdlàg D(Rl,Rd) retrieving particular results obtained [59] stationary real line removing l=1 therein. Further, potential applications open questions.