Thus, for example, if the uniform asymptotic negligibility ( u . a . n . ) condition is satisfied via an appropriate scaling of identically distributed random variables with finite variance, the weak convergence is to the normal distribution in the classical version of the central limit theorem.
22.
For any Borel subset " A " of " X " . ( The equality of the two integrals follows from Fubini's theorem . ) With respect to the topology of weak convergence of measures, the operation of convolution makes the space of probability measures on " X " into a topological semigroup.
