Theorems · Theorem · measure theory
MeasureTheory.laverage_mono_ae
∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f g : α → ENNReal},
f ≤ᵐ[μ] g → ⨍⁻ (a : α), f a ∂μ ≤ ⨍⁻ (a : α), g a ∂μ- Defined in
- Mathlib.MeasureTheory.Integral.Average
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 177 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.
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- MeasureTheory.aestatement and proof · cited by 2,352
- Filter.EventuallyLEstatement and proof · cited by 383
- Filter.Eventually.filter_monoproof · cited by 84
- MeasureTheory.laveragestatement · cited by 44
- MeasureTheory.lintegral_mono_aeproof · cited by 36
- MeasureTheory.Measure.smul_absolutelyContinuousproof · cited by 11
- MeasureTheory.Measure.ae_mono'proof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.setLAverage_le_essSupproof · cited by 1
- MeasureTheory.setLAverage_mono_aeproof · cited by 0