When talking of functions that are Riemann integrable but not Lebesgue integrable we always give the example of $f(x)=\frac{\sin(x)}{x}$ on $]0,\infty [$ but my question is : is it the same with $f(x)=x$ on $]-\infty,\infty [$ and if so why never use this as an example??
2026-04-02 19:43:40.1775159020
a Very simple example
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$f(x)=x$ is not Riemann integrable, in improper sense, or Lebesgue integrable.