If a function is Lebesgue integrable, is it possible that it has as set of discontinuity points measure bigger than zero?
2026-04-01 17:31:51.1775064711
Lebesgue integrable discontinuity points
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Yes. The set of discontinuity points can even be the whole space. For instance, $1_{\mathbb{Q}}$ is Lebesgue integrable, with its integral being $m(\mathbb{Q})=0$.