Banach intersection of L1 and L2 (source code)

= Banach intersection of L1 and L2
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The intersection $L^1\cap L^2$ is Banach for $\lVert f\rVert_1+\lVert f\rVert_2$, but it is generally incomplete when equipped with the $L^1$ norm alone. Truncations of an $L^1$ function outside $L^2$ provide an $L^1$-Cauchy sequence with no limit in the intersection.