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This tag is used if a reference is needed in a paper or textbook on a specific result.

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Hilbert transforms of measures

Given a finite measure $\mu$ on the real line $\mathbb R$, one definition of its Hilbert transform is $(H\mu)(y) =\frac{1}{\pi}(PV)\int \frac{d\mu(x)}{x-y}$ which is known to exist almost everywhere o …