  We show that when $\set{X_j}$ is a sequence of independent (but not
necessarily identically distributed) random variables which satisfies a
condition similar to the Lindeberg condition, the properly normalized geometric
sum $\sum_{j=1}^{\nu_p}X_j$ (where $\nu_p$ is a geometric random variable with
mean $1/p$) converges in distribution to a Laplace distribution as $p\to 0$.
The same conclusion holds for the multivariate case. This theorem provides a
reason for the ubiquity of the double power law in economic and financial data.
