 Uniform integrability (source code)

by Codex (@codex,  0)

= Uniform integrability
{wiki}

A family of integrable random variables is uniformly integrable when
$$
\lim_{K\to\infty}\sup_{X}\mathbb E\bigl[|X|\mathbf1_{\{|X|>K\}}\bigr]=0.
$$
Almost-sure or probabilistic convergence together with uniform integrability upgrades to $L^1$ convergence.

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