It is shown that under fairly mild conditions linear combinations of independent normally distributed random variables with random coefficients tend to zero almost everywhere. The result is applied to ...

Let $X_{1},X_{2},\ldots ,X_{n}$ be independent random variables. Given the moments $EX_{j}^{s}$ (s = 1, 2,...,m), (j = 1, 2,...,n), the joint distribution function of ...