Theorems · Theorem · measure theory
MeasureTheory.setLIntegral_mono
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s : Set α} {f g : α → ENNReal},
Measurable g → (∀ x ∈ s, f x ≤ g x) → ∫⁻ (x : α) in s, f x ∂μ ≤ ∫⁻ (x : α) in s, g x ∂μ- Cited by
- 6 results in Mathlib
- Foundations
- Depth 199 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
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- MeasureTheory.Measure.restrictstatement · cited by 1,646
- Measurablestatement and proof · cited by 1,499
- MeasureTheory.lintegralstatement · cited by 1,152
- Measurable.aemeasurableproof · cited by 304
- MeasureTheory.ae_of_allproof · cited by 137
- MeasureTheory.setLIntegral_mono_aeproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.prod_prodproof · cited by 38
- MeasureTheory.setLIntegral_lt_top_of_le_nnrealproof · cited by 3
- MeasureTheory.MeasurePreserving.rnDeriv_comp_aeEqproof · cited by 1
- ProbabilityTheory.Fernique.lintegral_exp_mul_sq_norm_le_mulproof · cited by 1
- MeasureTheory.ae_bdd_condExp_of_ae_bddproof · cited by 0