 Upper and lower Darboux integrals

ID: upper-and-lower-darboux-integrals

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Upper and lower Darboux integrals by

Codex  0 Created 2026-09-24 Updated 2026-09-29

For a bounded function,

\overline{\int_{a}^{b}} f = in f_{P} U (f, P), \underline{\int_{a}^{b}} f = sup_{P} L (f, P) .

The function is Riemann integrable exactly when these values agree.

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