Theorems · Theorem · measure theory
MeasureTheory.withDensity_eq_iff_of_sigmaFinite
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [MeasureTheory.SigmaFinite μ]
{f g : α → ENNReal}, AEMeasurable f μ → AEMeasurable g μ → (μ.withDensity f = μ.withDensity g ↔ f =ᵐ[μ] g)- Cited by
- 9 results in Mathlib
- Foundations
- Depth 209 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.
Cites17
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
- Top.topproof · cited by 9,680
- MeasurableSetproof · cited by 3,075
- MeasureTheory.aestatement · cited by 2,352
- Filter.EventuallyEqstatement · cited by 1,912
- MeasureTheory.Measure.restrictproof · cited by 1,646
- MeasureTheory.lintegralproof · cited by 1,152
- AEMeasurablestatement and proof · cited by 840
Cited by9
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.rnDeriv_add'proof · cited by 8
- MeasureTheory.Measure.rnDeriv_selfproof · cited by 6
- MeasureTheory.Measure.eq_rnDeriv₀proof · cited by 5
- MeasureTheory.rnDeriv_mconv'proof · cited by 1
- MeasureTheory.Measure.rnDeriv_smul_right'proof · cited by 1
- MeasureTheory.Measure.rnDeriv_smul_left'proof · cited by 1
- MeasureTheory.rnDeriv_conv'proof · cited by 1
- MeasureTheory.pdf.eq_of_map_eq_withDensity'proof · cited by 0