Theorems · Theorem · measure theory
MeasureTheory.ae_restrict_union_eq
∀ {α : Type u_2} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} (s t : Set α),
MeasureTheory.ae (μ.restrict (s ∪ t)) = MeasureTheory.ae (μ.restrict s) ⊔ MeasureTheory.ae (μ.restrict t)- 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.
Cites11
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
- Filterstatement · cited by 8,121
- Set.iUnionproof · cited by 2,483
- MeasureTheory.aestatement and proof · cited by 2,352
- MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
- MeasureTheory.ae.congr_simpproof · cited by 39
- Set.union_eq_iUnionproof · cited by 28
- iSup_bool_eqproof · cited by 12
- MeasureTheory.ae_restrict_iUnion_eqproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.ae_restrict_uIoc_eqproof · cited by 1
- MeasureTheory.ae_restrict_union_iffproof · cited by 1