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Theorems · Theorem · measure theory

MeasureTheory.ae_eq_refl

∀ {α : Type u_1} {β : Type u_2} {F : Type u_3} [inst : FunLike F (Set α) ENNReal]
  [inst_1 : MeasureTheory.OuterMeasureClass F α] {μ : F} (f : α → β), f =ᵐ[μ] f
Defined in
Mathlib.MeasureTheory.OuterMeasure.AE
Cited by
29 results in Mathlib
Foundations
Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FunLikeMeasureTheory.OuterMeasureClass

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Measurable.aemeasurable · cited by 304Measurable.aemeasurableMeasureTheory.lintegral_add_left' · cited by 11MeasureTheory.lintegral_a…MeasureTheory.Measure.restrict_apply₀' · cited by 7Measure.restrict_apply₀'MeasureTheory.union_ae_eq_left_of_ae_eq_empty · cited by 4MeasureTheory.union_ae_eq…MeasureTheory.union_ae_eq_right_of_ae_eq_empty · cited by 4MeasureTheory.union_ae_eq…MeasureTheory.isClosed_setOfPred_preimage_ae_eq · cited by 3MeasureTheory.isClosed_se…MeasureTheory.Ioo_ae_eq_Ico' · cited by 3MeasureTheory.Ioo_ae_eq_I…MeasureTheory.Ioo_ae_eq_Ioc' · cited by 3MeasureTheory.Ioo_ae_eq_I…MeasureTheory.FinStronglyMeasurable.aefinStronglyMeasurable · cited by 2FinStronglyMeasurable.aef…MeasureTheory.Ico_ae_eq_Icc' · cited by 2MeasureTheory.Ico_ae_eq_I…MeasureTheory.Ioc_ae_eq_Icc' · cited by 2MeasureTheory.Ioc_ae_eq_I…blimsup_cthickening_mul_ae_eq · cited by 2blimsup_cthickening_mul_a…MeasureTheory.Measure.isEverywherePos_everywherePosSubset_of_measure_ne_top · cited by 2Measure.isEverywherePos_e…MeasureTheory.NullMeasurableSet.exists_isOpen_symmDiff_lt · cited by 1NullMeasurableSet.exists_…MeasureTheory.Measure.measure_toMeasurable_inter_of_cover · cited by 1Measure.measure_toMeasura…Set · cited by 53352SetENNReal · cited by 9879ENNRealFunLike · cited by 2560FunLikeMeasureTheory.ae · cited by 2352MeasureTheory.aeFilter.EventuallyEq · cited by 1912Filter.EventuallyEqMeasureTheory.OuterMeasureClass · cited by 104MeasureTheory.OuterMeasur…Filter.EventuallyEq.rfl · cited by 55EventuallyEq.rflMeasureTheory.ae_eq_reflCITED BYCITES

Cites7

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Cited by29

Results whose statement or proof uses this declaration.