For two random variables $X_1$ and $X_2$, we know that $|X_1+X_2|$$\le |X_1|+|X_2|$, where $|.|$ means the $L_p$ norm, by Minkowski’s inequality. To what extent, can this be extended to an infinite sum? Suppose that the infinite sum of $L_p$ norms is summable.
2026-05-15 10:43:10.1778841790
$L_p$ norm of a infinite sum
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