How do I prove that the function $$f(x)= \begin{cases} 1-x &,\text{when}\; x \;\text{is rational} \\ 1/x &, \text{when}\; x \;\text{is irrational} \end{cases}$$ is not integrable on every interval $[a,b]$?
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1Riemann or Lebesgue integral? – Brian Tung Dec 16 '18 at 21:17
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By the definition of integral, it is easy to check that for any partition of [a,b], the upper integral never equals the lower integral. Thus the function not integrable.
Alvis Nordkovich
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