How to show the below theorem? In fact ,I feel it is not right , if $f(x)\ne 0 $ at zero measure set , I still have $$ \int_\Omega f(x)\varphi(x)dx = 0 ~~~\forall \varphi \in C^\infty_0(\Omega) $$ What is my mistake ?
2026-04-06 01:51:08.1775440268
Weakly convergence and pointwise convergence of $L^2$
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