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Methods for bounding oscillatory integrals

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This page contains links to articles about bounding integrals by exploiting cancellation in the integrand. If for some reason one does not believe that one can, should, or need to exploit cancellation, one can of course just use the triangle inequality

 |\int_E f(x)\ d\mu(x)| \leq \int_E |f(x)|\ d|\mu|(x)

and use methods for bounding non-oscillatory integrals instead.