Theorems · Theorem · measure theory
MeasureTheory.ae_restrict_union_iff
∀ {α : Type u_2} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} (s t : Set α) (p : α → Prop),
(∀ᵐ (x : α) ∂μ.restrict (s ∪ t), p x) ↔ (∀ᵐ (x : α) ∂μ.restrict s, p x) ∧ ∀ᵐ (x : α) ∂μ.restrict t, p x- Defined in
- Mathlib.MeasureTheory.Measure.Restrict
- Cited by
- 1 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.
Cites7
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
- MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
- MeasureTheory.ae_restrict_union_eqproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- ae_restrict_of_ae_restrict_inter_Iooproof · cited by 0