Weak convergence and the Prokhorov radius

Abstract

The Prokhorov radius for a set of probability measures satisfying basic moment conditions is introduced, through the Prokhorov distance of these measures from the Dirac measure at a fixed point of the real line. This is calculated precisely by the use of standard tools from the Kemperman geometric moment theory. The above radius gives the exact rate of weak convergence of these measures to the Dirac measure.