Theorems · Theorem · measure theory
intervalIntegral.integral_nonneg_of_ae_restrict
∀ {f : ℝ → ℝ} {a b : ℝ} {μ : MeasureTheory.Measure ℝ},
a ≤ b → 0 ≤ᵐ[μ.restrict (Set.Icc a b)] f → 0 ≤ ∫ (u : ℝ) in a..b, f u ∂μ- Cited by
- 3 results in Mathlib
- Foundations
- Depth 254 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- NormedAddCommGroupproof · cited by 15,752
- NormedSpaceproof · cited by 12,499
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Filter.Eventuallyproof · cited by 3,134
- MeasureTheory.aestatement and proof · cited by 2,352
- Set.Iccstatement and proof · cited by 1,702
- MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
- Set.Iocproof · cited by 971
- intervalIntegralstatement · cited by 546
- Filter.EventuallyLEstatement and proof · cited by 383
- intervalIntegral.integral_of_leproof · cited by 83
Cited by3
Results whose statement or proof uses this declaration.
- intervalIntegral.integral_nonnegproof · cited by 3
- intervalIntegral.integral_nonneg_of_aeproof · cited by 1
- MonotoneOn.intervalIntegral_deriv_mem_uIccproof · cited by 0