Theorems · Theorem · measure theory
MeasureTheory.ae.congr_simp
∀ {α : Type u_1} {F : Type u_3} [inst : FunLike F (Set α) ENNReal] [inst_1 : MeasureTheory.OuterMeasureClass F α]
(μ μ_1 : F), μ = μ_1 → MeasureTheory.ae μ = MeasureTheory.ae μ_1- Defined in
- Mathlib.MeasureTheory.OuterMeasure.AE
- Cited by
- 39 results in Mathlib
- Foundations
- Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- ENNRealstatement and proof · cited by 9,879
- Filterstatement · cited by 8,121
- FunLikestatement and proof · cited by 2,560
- MeasureTheory.aestatement and proof · cited by 2,352
- MeasureTheory.OuterMeasureClassstatement and proof · cited by 104
Cited by39
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.rnDeriv_eq_zero_of_mutuallySingularproof · cited by 5
- intervalIntegral.integral_deriv_of_contDiffOn_Iccproof · cited by 4
- ProbabilityTheory.condDistrib_ae_eq_of_measure_eq_compProdproof · cited by 4
- MeasureTheory.ae_toFiniteproof · cited by 3
- MeasureTheory.condExp_stronglyMeasurable_bilin_of_boundproof · cited by 3
- MeasureTheory.toReal_rnDeriv_trimproof · cited by 3
- MeasureTheory.setToFun_measure_zeroproof · cited by 3
- MeasureTheory.ae_restrict_of_ae_eq_of_ae_restrictproof · cited by 2
- MeasureTheory.ae_restrict_union_eqproof · cited by 2
- ProbabilityTheory.Kernel.ae_compProd_of_ae_aeproof · cited by 2
- ProbabilityTheory.condDistrib_comp_selfproof · cited by 2
- MeasureTheory.AEMeasurable.ae_eq_of_forall_setLIntegral_eqproof · cited by 2