Theorems · Theorem · measure theory
ContinuousOn.intervalIntegrable_of_Icc
∀ {E : Type u_5} [inst : NormedAddCommGroup E] {μ : MeasureTheory.Measure ℝ} [MeasureTheory.IsLocallyFiniteMeasure μ]
{u : ℝ → E} {a b : ℝ}, a ≤ b → ContinuousOn u (Set.Icc a b) → IntervalIntegrable u μ a b- Cited by
- 5 results in Mathlib
- Foundations
- Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Set.Iccstatement and proof · cited by 1,702
- ContinuousOnstatement and proof · cited by 1,411
- IntervalIntegrablestatement · cited by 316
- MeasureTheory.IsLocallyFiniteMeasurestatement and proof · cited by 171
- Set.uIcc_of_leproof · cited by 54
- ContinuousOn.intervalIntegrableproof · cited by 27
Cited by5
Results whose statement or proof uses this declaration.
- intervalIntegral.integral_deriv_of_contDiffOn_Iccproof · cited by 4
- intervalIntegral.integral_unitInterval_deriv_eq_subproof · cited by 2
- HasFDerivWithinAt.curveIntegral_segment_source'proof · cited by 2
- intervalIntegral.integral_lt_integral_of_continuousOn_of_le_of_exists_ltproof · cited by 2
- ContinuousOn.curveIntegrable_of_contDiffOnproof · cited by 0