Real Analysis II · Integration
Dense discontinuities with integrability
Problem
Let t(x)=1/q when x=p/q in lowest terms and t(x)=0 for irrational x on [0,1]. Prove t is Riemann integrable with integral 0.
Hint
In “Dense discontinuities with integrability,” first rewrite the requested conclusion using tagged sums, oscillation, or total variation.
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