We define a new class of positive and measurable functions in terms of their asymptotic behavior at infinity. This new class extends the class of regularly varying functions, for broader applications. We provide different characterizations of the new class and consider integrals, convolutions and Laplace transforms. We give some applications in probability theory. Some natural extensions of the new class are also derived.
CADENA, M., KRATZ, M. et OMEY, E. (2017). On the Order of Functions at Infinity. Journal of Mathematical Analysis and Applications, 452(1), pp. 109-125.