Prove that $\sum_{k=1}^{\infty}X_k a_{n,k}$ exists almost surely for each $n$.
Is it that $P\bigg(\displaystyle\lim_{n\rightarrow\infty}\sum_{k=1}^{\infty}X_ka_{n,k}<\infty\bigg)=1$?
In this case $X_k$ is a sequence of random variables and $a_{n,k}$ are elements of a regular matrix.
I'm just confused on the wording, thanks!