Real Analysis II · Integration
Cauchy criterion for sums
Problem
Assume a bounded function f on [a,b] has the following property: for every ε>0 there is δ>0 such that any two tagged sums with mesh below δ differ by less than ε. Prove f is Riemann integrable.
Hint
Treat all sufficiently fine tagged sums as a net indexed by refinements.
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