Theorems · Theorem · measure theory
MeasureTheory.ae_restrict_of_ae_restrict_of_subset
∀ {α : Type u_2} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s t : Set α} {p : α → Prop},
s ⊆ t → (∀ᵐ (x : α) ∂μ.restrict t, p x) → ∀ᵐ (x : α) ∂μ.restrict s, p x- Defined in
- Mathlib.MeasureTheory.Measure.Restrict
- Cited by
- 8 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.
Cites10
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
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Filter.Eventuallystatement and proof · cited by 3,134
- MeasureTheory.aestatement and proof · cited by 2,352
- le_reflproof · cited by 2,061
- MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
- Filter.Eventually.filter_monoproof · cited by 84
- MeasureTheory.Measure.restrict_monoproof · cited by 33
- MeasureTheory.ae_monoproof · cited by 22
Cited by8
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.eqOn_of_ae_eqproof · cited by 4
- MeasureTheory.setIntegral_eq_of_subset_of_ae_sdiff_eq_zeroproof · cited by 4
- intervalIntegral.integral_nonneg_of_ae_restrictproof · cited by 3
- integrableOn_mul_sum_Iccproof · cited by 3
- VitaliFamily.ae_tendsto_measure_inter_divproof · cited by 2
- MeasureTheory.lintegral_comp_eq_lintegral_meas_le_mul_of_measurableproof · cited by 1
- ae_restrict_of_ae_restrict_inter_Iooproof · cited by 0
- intervalIntegral.continuousAt_parametric_primitive_of_dominatedproof · cited by 0