Theorems · Theorem · measure theory
MeasureTheory.ae_imp_of_ae_restrict
∀ {α : Type u_2} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s : Set α} {p : α → Prop},
(∀ᵐ (x : α) ∂μ.restrict s, p x) → ∀ᵐ (x : α) ∂μ, x ∈ s → p x- Defined in
- Mathlib.MeasureTheory.Measure.Restrict
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Set.ofPredproof · cited by 6,101
- Filter.Eventuallystatement and proof · cited by 3,134
- MeasureTheory.aestatement and proof · cited by 2,352
- MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
- Set.inter_commproof · cited by 291
- MeasureTheory.Measure.measure_inter_eq_zero_of_restrictproof · cited by 2
Cited by12
Results whose statement or proof uses this declaration.
- intervalIntegral.integral_congr_ae_restrictproof · cited by 6
- MeasureTheory.setIntegral_eq_of_subset_of_ae_sdiff_eq_zeroproof · cited by 4
- MeasureTheory.Measure.eqOn_open_of_ae_eqproof · cited by 2
- MeasureTheory.condExp_bilin_of_stronglyMeasurable_leftproof · cited by 2
- MeasureTheory.VectorMeasure.setIntegral_eq_zero_of_ae_eq_zeroproof · cited by 1
- MeasureTheory.integral_union_eq_left_of_ae_auxproof · cited by 1
- MeasureTheory.le_ae_restrictproof · cited by 1
- MeasureTheory.setIntegral_eq_zero_of_ae_eq_zeroproof · cited by 1
- MeasureTheory.AEStronglyMeasurable.ae_mem_imp_eq_mkproof · cited by 1
- MeasureTheory.nullMeasurableSet_restrict_of_subsetproof · cited by 0
- AEMeasurable.ae_mem_imp_eq_mkproof · cited by 0
- intervalIntegral.continuousAt_parametric_primitive_of_dominatedproof · cited by 0