Theorems · Theorem · measure theory
MeasureTheory.ae_eq_empty
∀ {α : Type u_1} {F : Type u_3} [inst : FunLike F (Set α) ENNReal] [inst_1 : MeasureTheory.OuterMeasureClass F α]
{μ : F} {s : Set α}, s =ᵐ[μ] ∅ ↔ μ s = 0- Defined in
- Mathlib.MeasureTheory.OuterMeasure.AE
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 137 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- ENNRealstatement and proof · cited by 9,879
- Set.ofPredproof · cited by 6,101
- FunLikestatement and proof · cited by 2,560
- MeasureTheory.aestatement · cited by 2,352
- Filter.EventuallyEqstatement · cited by 1,912
- MeasureTheory.OuterMeasureClassstatement and proof · cited by 104
- Filter.eventuallyEq_emptyproof · cited by 2
Cited by17
Results whose statement or proof uses this declaration.
- MeasureTheory.NullMeasurableSet.of_nullproof · cited by 7
- MeasureTheory.lintegral_image_eq_lintegral_deriv_mul_of_monotoneOnproof · cited by 3
- MeasureTheory.ae_bdd_norm_condExp_of_ae_bdd_normproof · cited by 2
- AddCircle.ae_empty_or_univ_of_forall_vadd_ae_eq_selfproof · cited by 2
- AddCircle.closedBall_ae_eq_ballproof · cited by 2
- MeasureTheory.integral_image_eq_integral_deriv_smul_of_monotoneOnproof · cited by 2
- MeasureTheory.lintegral_abs_det_fderiv_eq_addHaar_image₀proof · cited by 1
- MeasureTheory.integral_divergence_of_hasFDerivAt_off_countableproof · cited by 1
- indicator_meas_zeroproof · cited by 1
- NumberField.mixedEmbedding.iUnion_negAt_plusPart_aeproof · cited by 1
- MeasureTheory.laverage_union_mem_segmentproof · cited by 0