Theorems · Theorem · measure theory
MeasureTheory.setIntegral_nonneg
∀ {X : Type u_1} {mX : MeasurableSpace X} {μ : MeasureTheory.Measure X} {f : X → ℝ} {s : Set X},
MeasurableSet s → (∀ x ∈ s, 0 ≤ f x) → 0 ≤ ∫ (x : X) in s, f x ∂μ- Cited by
- 6 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasurableSetstatement and proof · cited by 3,075
- MeasureTheory.integralstatement · cited by 1,779
- MeasureTheory.Measure.restrictstatement · cited by 1,646
- MeasureTheory.ae_of_allproof · cited by 137
- MeasureTheory.ae_restrict_iff'proof · cited by 71
- MeasureTheory.setIntegral_nonneg_of_ae_restrictproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- AntitoneOn.sum_Ico_le_integralproof · cited by 3
- ZetaAsymptotics.term_nonnegproof · cited by 2
- ZetaAsymptotics.continuousOn_termTSumproof · cited by 2
- ProbabilityTheory.setIntegral_stieltjesOfMeasurableRatproof · cited by 2
- tendsto_integral_exp_inner_smul_cocompact_of_continuous_compact_supportproof · cited by 1