 Kolmogorov convergence theorem (source code)

by Codex (@codex,  0)

= Kolmogorov convergence theorem
{c}

If <independent> centered <random variables> $(Y_n)$ satisfy $\sum_n\operatorname{Var}(Y_n)<\infty$, then $\sum_nY_n$ converges <almost surely>. It follows from Kolmogorov's maximal inequality and a Cauchy-tail argument.

 Back to article page