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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, ...
13
votes
Why should one still teach Riemann integration?
Although not a direct answer to the question, this may be relevant to the discussion:
I learnt basic measure theory and the theory of Lebesgue integration in a course called "Probability and Measure" …