Let $f$ be analytic on a domain $\Omega$ of the complex plane, such that the closed disc $\overline{D(0,R)}$ is contained in $\Omega$. What is the difference between $$ \int_{D(0,R)}|f(w)|dm(w)$$ and $$\iint_{D(0,R)}|f(x,y)|dxdy$$ where $dm$ is the Lebesgue measure in $\mathbb R^2=\mathbb C$?
2026-05-16 20:12:11.1778962331
Riemann integral vs Lebesgue integral
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