Theorems · Theorem · measure theory
MeasureTheory.Measure.restrict_toOuterMeasure_eq_toOuterMeasure_restrict
∀ {α : Type u_2} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s : Set α},
MeasurableSet s → (μ.restrict s).toOuterMeasure = (MeasureTheory.OuterMeasure.restrict s) μ.toOuterMeasureThis lemma shows that restrict and toOuterMeasure commute. Note that the LHS has a
restrict on measures and the RHS has a restrict on outer measures.
- Defined in
- Mathlib.MeasureTheory.Measure.Restrict
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 193 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- RingHom.idstatement · cited by 18,349
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- LinearMapstatement · cited by 10,215
- ENNRealstatement · cited by 9,879
- MeasurableSetstatement and proof · cited by 3,075
- MeasureTheory.Measure.restrictstatement · cited by 1,646
- MeasureTheory.OuterMeasurestatement and proof · cited by 287
- MeasureTheory.Measure.toOuterMeasurestatement and proof · cited by 75
- MeasureTheory.OuterMeasure.restrictstatement and proof · cited by 20
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.restrict_apply'proof · cited by 32
- MeasureTheory.Measure.restrict_sInf_eq_sInf_restrictproof · cited by 1