Theorems · Theorem · measure theory
intervalIntegral.integral_nonneg
∀ {f : ℝ → ℝ} {a b : ℝ} {μ : MeasureTheory.Measure ℝ},
a ≤ b → (∀ u ∈ Set.Icc a b, 0 ≤ f u) → 0 ≤ ∫ (u : ℝ) in a..b, f u ∂μ- Cited by
- 3 results in Mathlib
- Foundations
- Depth 255 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.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Set.Iccstatement and proof · cited by 1,702
- intervalIntegralstatement · cited by 546
- MeasureTheory.ae_of_allproof · cited by 137
- MeasureTheory.ae_restrict_iff'proof · cited by 71
- measurableSet_Iccproof · cited by 32
- intervalIntegral.integral_nonneg_of_ae_restrictproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- le_radius_cauchyPowerSeriesproof · cited by 2
- Chebyshev.integral_theta_div_log_sq_isBigOproof · cited by 2
- ProbabilityTheory.sum_prob_mem_Ioc_leproof · cited by 1