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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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How to define integration for general functions?

Usually integration is defined for real-valued function $f$ or complex-value function, (which is essentially same as real-valued one). … In order to make it more "useful", it's better to related this definite integration to some formal indefinite integrations such as discussed here …
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