Can you please help me to prove that function $f(x) = \frac{1}{x}$ is non-integrable in the sense of the Lebesgue integral on $x \in (0; 1)$
2026-03-30 08:21:16.1774858876
Lebesgue nonintegrability
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Riemann integrable functions are also Lebesgue integral with the same integral. Hence the Lebesgue integral $\int_{\epsilon}^{1}\frac 1 xdx=-\log\, \epsilon \to \infty$. Hence the Lebesgue integral is $\infty$.