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Questions related to various forms of integration including the Riemann integral, Lebesgue integral, Riemann–Stieltjes integral, double integrals, line integrals, contour integrals, surface integrals, integrals of differential forms, ...

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Convergence of oscillatory integrals

I'm considering integrals of the (Hilbert transform) type $$p.v.\int_{-\infty}^\infty\frac{f(r)}{r}\,dr$$ where $f(r)$ is periodic, say, with period $2\pi$. I'm assuming very little regularity on $f$. …
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