Theorems · Theorem · measure theory
MeasureTheory.ae_le_of_forall_setLIntegral_le_of_sigmaFinite
∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} [MeasureTheory.SigmaFinite μ]
{f g : α → ENNReal},
Measurable f →
(∀ (s : Set α), MeasurableSet s → μ s < ⊤ → ∫⁻ (x : α) in s, f x ∂μ ≤ ∫⁻ (x : α) in s, g x ∂μ) → f ≤ᵐ[μ] g- Cited by
- 6 results in Mathlib
- Foundations
- Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasureTheory.SigmaFinite
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.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- MeasurableSetstatement and proof · cited by 3,075
- MeasureTheory.aestatement · cited by 2,352
- MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
- Measurablestatement and proof · cited by 1,499
- MeasureTheory.lintegralstatement and proof · cited by 1,152
- MeasureTheory.SigmaFinitestatement and proof · cited by 526
Cited by6
Results whose statement or proof uses this declaration.
- ProbabilityTheory.preCDF_le_oneproof · cited by 4
- MeasureTheory.Measure.rnDeriv_le_one_of_leproof · cited by 2
- ProbabilityTheory.monotone_preCDFproof · cited by 1
- MeasureTheory.condLExp_smul_leproof · cited by 0
- MeasureTheory.condLExp_add_leproof · cited by 0
- MeasureTheory.condLExp_monoproof · cited by 0