Theorems · Theorem · measure theory
MeasureTheory.lintegral_mono_ae
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f g : α → ENNReal},
(∀ᵐ (a : α) ∂μ, f a ≤ g a) → ∫⁻ (a : α), f a ∂μ ≤ ∫⁻ (a : α), g a ∂μ- Cited by
- 36 results in Mathlib
- Foundations
- Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · 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
- Set.ofPredproof · cited by 6,101
- Filter.Eventuallystatement and proof · cited by 3,134
- MeasurableSetproof · cited by 3,075
- Compl.complproof · cited by 2,925
- iSupproof · cited by 2,415
- MeasureTheory.aestatement and proof · cited by 2,352
- MeasureTheory.lintegralstatement and proof · cited by 1,152
Cited by36
Results whose statement or proof uses this declaration.
- MeasureTheory.lintegral_congr_aeproof · cited by 95
- MeasurableEmbedding.lintegral_mapproof · cited by 10
- MeasureTheory.setLIntegral_mono_aeproof · cited by 5
- MeasureTheory.HasFiniteIntegral.mono_enormproof · cited by 5
- MeasureTheory.setLIntegral_mono_ae'proof · cited by 3
- MeasureTheory.eLpNorm_le_eLpNorm_top_mul_eLpNormproof · cited by 3
- MeasureTheory.eLpNorm'_le_eLpNormEssSup_mul_rpow_measure_univproof · cited by 3
- MeasureTheory.lintegral_tendsto_of_tendsto_of_monotoneproof · cited by 3
- MeasureTheory.eLpNorm'_mono_enorm_aeproof · cited by 3
- MeasureTheory.lintegral_add_mul_meas_add_le_le_lintegralproof · cited by 2
- MeasureTheory.laverage_mono_aeproof · cited by 2
- MeasureTheory.eLpNorm'_le_eLpNorm'_mul_eLpNorm'proof · cited by 2