APPROXIMATION OF PROBABILITY DISTRIBUTIONS BY CONVEX MIXTURES OF GAUSSIAN MEASURES

Let A(+) = {a = (a(n)) is an element of boolean AND(p>I) l(p) : a(n) > 0, for all(n) is an element of N} and let {171 be an enumeration of all normal distributions with mean a rational number and variance 1/n(2), a = 1,2 .... We prove that there exists an a is an element of A(+) such that that every probability density function, continuous, with compact support in R. can be approximated in L1 and L norm simultaneously by the averages 1/Sigma(n)(j=1)a(j) Sigma(n)(j=1) a(j)phi(j). The set of such sequences is a dense G(delta) set in A(+) and contains a dense positive cone.