Theorems · Theorem · measure theory
MeasureTheory.withDensity_congr_ae
∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f g : α → ENNReal},
f =ᵐ[μ] g → μ.withDensity f = μ.withDensity g- Cited by
- 19 results in Mathlib
- Foundations
- Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- MeasurableSetproof · cited by 3,075
- MeasureTheory.aestatement and proof · cited by 2,352
- Filter.EventuallyEqstatement and proof · cited by 1,912
- MeasureTheory.Measure.restrictproof · cited by 1,646
- MeasureTheory.lintegralproof · cited by 1,152
- MeasureTheory.Measure.extproof · cited by 308
- MeasureTheory.Measure.withDensitystatement and proof · cited by 265
Cited by19
Results whose statement or proof uses this declaration.
- MeasureTheory.withDensity_eq_iff_of_sigmaFiniteproof · cited by 9
- MeasureTheory.withDensity_eq_iffproof · cited by 6
- MeasureTheory.SigmaFinite.withDensity_of_ne_topproof · cited by 4
- MeasureTheory.lintegral_withDensity_eq_lintegral_mul₀'proof · cited by 3
- MeasureTheory.integrable_withDensity_iff_integrable_coe_smul₀proof · cited by 3
- MeasureTheory.integrable_withDensity_iff_integrable_smul'proof · cited by 3
- integral_withDensity_eq_integral_smul₀proof · cited by 3
- integral_withDensity_eq_integral_toReal_smul₀proof · cited by 3
- MeasureTheory.Measure.rnDeriv_eq_one_iff_eqproof · cited by 2
- MeasureTheory.withDensity_apply_eq_zero'proof · cited by 2
- MeasureTheory.lintegral_withDensity_eq_lintegral_mul_non_measurable₀proof · cited by 2
- MeasureTheory.integrable_withDensity_iff_integrable_smul₀'proof · cited by 2