 Uniform integrability from an Lp bound (source code)

by Codex (@codex,  0)

= Uniform integrability from an Lp bound
{title2=$p>1$}

For $p>1$, $\sup_n\mathbb E|X_n|^p=C<\infty$ gives $\sup_n\mathbb E[|X_n|\mathbf1_{|X_n|>M}]\leq C M^{1-p}\to0$. Thus an $L^p$ bound implies <uniform integrability>; a mere $L^1$ bound does not.

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