Infra-exponential
Introduction A growth rate is said to be '''infra-exponential''' or '''subexponential''' if it is dominated by all exponential growth rates, however great the doubling time. A continuous function with infra-exponential growth rate will have a Fourier transform that is a Fourier hyperfunction.Examples of subexponential growth rates arise in the analysis of algorithms, where they give rise to sub-exponential time complexity, and in the growth rate of groups, where a subexponential growth rate implies that a group is amenable.A positive-valued, unbounded probability distribution  may be called '''subexponential''' if its tails are heavy enough so that:See Heavy-tailed distribution#Subexponential distributions. Contrariwise, a random variable may also be called '''subexponential''' if its tails are sufficiently light to fall off at an exponential or faster rate.
References * Fourier hyperfunction in the Encyclopedia of Mathematics