I'm just looking for references about Riesz representation theorem for $L^p$ spaces and consequences.
Thank you very much.
2026-03-25 19:01:53.1774465313
Riesz representation theorem for $L^p$ spaces (References)
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Rudin's Real and Complex Analysis has a detailed discussion for it and there is a detailed 10 step proof provided as well (see pp. 40-47). He then defines the Lebesgue measure based on the Riesz Representation Theorem.
For the $L^p$ formulation you can have a look at Royden & Fitzpatrick's Real Analysis, 4e (e.g. pp. 160-161).