I'm having some trouble regarding a step in the proof as it appears in Stein's Real Analysis.
How is that the construction of $u$ guarantees that $u \in S$?. I obviously tried seeing that $l(u) = 0$ but ended nowhere.
2026-03-27 06:07:56.1774591676
Proof of Riesz's representation theorem in Stein's Real Analysis
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$\ell (f)$ and $\ell (h)$ are scalars. So linearity gives $\ell(u)=\ell (f)\ell (h)-\ell (h)\ell (f)=0$.