Theorems · Theorem · measure theory
MeasureTheory.withDensity_eq_iff
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f g : α → ENNReal},
AEMeasurable f μ → AEMeasurable g μ → ∫⁻ (x : α), f x ∂μ ≠ ⊤ → (μ.withDensity f = μ.withDensity g ↔ f =ᵐ[μ] g)- Cited by
- 6 results in Mathlib
- Foundations
- Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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.topstatement and proof · cited by 9,680
- Set.univproof · cited by 3,945
- 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.lintegralstatement and proof · cited by 1,152
Cited by6
Results whose statement or proof uses this declaration.
- MeasureTheory.pdf.eq_of_map_eq_withDensityproof · cited by 2
- MeasureTheory.Measure.rnDeriv_smul_leftproof · cited by 2
- MeasureTheory.Measure.rnDeriv_smul_rightproof · cited by 2
- MeasureTheory.rnDeriv_convproof · cited by 1
- MeasureTheory.Measure.rnDeriv_addproof · cited by 1
- MeasureTheory.rnDeriv_mconvproof · cited by 1