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 ...

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 ...