$\|f_k\|_p\to \|f\|_p$: Is there a name for this type of convergence?
What I know is convergence in $L^p$ norm usually means $\|f-f_k\|_p\to 0$, which is different from the above.
Thanks!
2026-04-07 16:30:54.1775579454
What is this mode of convergence called?
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I'm not sure this is really convergence in any reasonable sense, it's just saying the two of them are on the same radius sphere, so if I were to call it anything, I'd say it's convergence as a sequence of real numbers, i.e. if $a_k=\lVert f_k\rVert_p\in\Bbb R$ then $a_k\to a=\lVert f\rVert_p\in\Bbb R$.