fix: nonempty/closed hypotheses for Riemann and Darboux integrability#609
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Chessing234 wants to merge 6 commits into
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fix: nonempty/closed hypotheses for Riemann and Darboux integrability#609Chessing234 wants to merge 6 commits into
Chessing234 wants to merge 6 commits into
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RiemannIntegrableOn needs I.toSet.Nonempty; continuous/piecewise_continuous omitted it, so empty Icc a b with a > b made the conclusions false. Co-authored-by: Cursor <cursoragent@cursor.com>
Empty reversed intervals made DarbouxIntegrableOn hold vacuously while RiemannIntegrableOn failed, so iff_darbouxIntegrable was false. Co-authored-by: Cursor <cursoragent@cursor.com>
indicator_of_elem claimed RiemannIntegrableOn on any BoundedInterval; open intervals make the conclusion false, and riemann_integral_of_elem then returned the junk value 0 instead of the Jordan measure. Co-authored-by: Cursor <cursoragent@cursor.com>
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Summary
RiemannIntegrableOn.continuous/piecewise_continuousomittedI.toSet.Nonempty, so empty reversedIccmade the conclusions false.DarbouxIntegrableOnlacked nonempty (and buriedLower = Upperunder∀), soiff_darbouxIntegrablefailed on empty intervals.indicator_of_elem/riemann_integral_of_elemclaimed Riemann integrability on arbitraryBoundedInterval; openImakes the claims false (junk integral0).Feature branches:
fix/riemann-cts-nonempty,fix/darboux-nonempty,fix/riemann-indicator-closed.Test plan
lake build Analysis.MeasureTheory.Section_1_1_3Made with Cursor