Is there a term for a sequence of random variables with the following property:
$$\mathbb{E} \left[ \sum_{i = 1}^\infty X_i^2 \right] < \infty$$
The current language I'm using is that $X$ is square-summable almost surely, but really that should mean this:
$$P\left(\sum_{i = 1}^\infty X_i^2 < \infty \right) = 1$$
which is a slightly weaker claim. There are so many terms for forms of convergence weaker than almost sure convergence--where are all the terms for stronger forms?