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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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measurability of integrated functions
I know in computable analysis, which is closely related to the descriptive set theoretic questions you are asking, that the Lévy–Prokhorov metric on the weak topology is useful. (I think the narrow t …