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Mathematics
Topology and Analysis
Original definition of Riemann Integral and Darboux Sums
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[QUOTE="lavinia, post: 6842201, member: 243745"] [USER=696593]@Hall[/USER] This is a nice proof but I don't see how it proves that a continuous function is Riemann integrable. It seems rather to show that if one computes the Riemann sums at the two end points of each interval in a partition,then their difference converges to zero. You seem to want to prove that the upper and lower sums converge to each other but then the function is evaluated at its maximum and minimum on each interval in the partition not at the endpoints. This said, I think your proof has the right idea and can be easily modified. [/QUOTE]
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Original definition of Riemann Integral and Darboux Sums
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