Theorems · Theorem · measure theory
MeasureTheory.Measure.exists_mem_of_measure_ne_zero_of_ae
∀ {α : Type u_2} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s : Set α},
μ s ≠ 0 → ∀ {p : α → Prop}, (∀ᵐ (x : α) ∂μ.restrict s, p x) → ∃ x ∈ s, p x- Defined in
- Mathlib.MeasureTheory.Measure.Restrict
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- 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
- Filter.Frequently.and_eventuallyproof · cited by 49
- Filter.Frequently.existsproof · cited by 32
- MeasureTheory.Measure.restrict_apply_selfproof · cited by 7
- MeasureTheory.frequently_ae_mem_iffproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- AddCircle.ae_empty_or_univ_of_forall_vadd_ae_eq_selfproof · cited by 2
- blimsup_cthickening_ae_le_of_eventually_mul_le_auxproof · cited by 1