Theorems · Theorem · measure theory
MeasureTheory.Measure.map_congr
∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {μ : MeasureTheory.Measure α}
{f g : α → β}, f =ᵐ[μ] g → MeasureTheory.Measure.map f μ = MeasureTheory.Measure.map g μ- Defined in
- Mathlib.MeasureTheory.Measure.Map
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 198 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.
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasureTheory.aestatement and proof · cited by 2,352
- Filter.EventuallyEqstatement and proof · cited by 1,912
- MeasureTheory.Measure.mapstatement · cited by 858
- AEMeasurableproof · cited by 840
- Filter.EventuallyEq.symmproof · cited by 408
- Filter.EventuallyEq.transproof · cited by 123
- AEMeasurable.ae_eq_mkproof · cited by 65
- AEMeasurable.measurable_mkproof · cited by 62
- MeasureTheory.Measure.map_of_not_aemeasurableproof · cited by 21
- AEMeasurable.congrproof · cited by 10
Cited by17
Results whose statement or proof uses this declaration.
- MeasureTheory.integral_mapproof · cited by 67
- MeasureTheory.lintegral_map'proof · cited by 14
- ProbabilityTheory.condDistrib_ae_eq_of_measure_eq_compProdproof · cited by 4
- ProbabilityTheory.condDistrib_congrproof · cited by 3
- ProbabilityTheory.IdentDistrib.of_ae_eqproof · cited by 3
- ProbabilityTheory.hasLaw_smul_dirac_of_ae_eqproof · cited by 2
- ProbabilityTheory.HasLaw.congrproof · cited by 2
- MeasureTheory.Measure.bind_congr_rightproof · cited by 2
- ProbabilityTheory.map_restrict_eq_of_forall_ae_eqproof · cited by 2
- MeasureTheory.Measure.QuasiMeasurePreserving.congrproof · cited by 1
- MeasureTheory.Measure.restrict_map_of_aemeasurableproof · cited by 1
- MeasureTheory.MeasurePreserving.congrproof · cited by 1