We define a new class of positive and Lebesgue measurable functions in terms of their asymptotic behavior, which includes the class of regularly varying functions. We also characterize it by transformations, corresponding to generalized moments when these functions are random variables. We study the properties of this new class and discuss their applications to Extreme Value Theory.
KRATZ, M. and CADENA, M. (2014). An Extension of the Class of Regularly Varying Functions. ESSEC Business School.