Theorems · Theorem · measure theory
MeasureTheory.Measure.iSup_restrict_spanningSets_of_measurableSet
∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s : Set α}
[inst : MeasureTheory.SigmaFinite μ], MeasurableSet s → ⨆ i, (μ.restrict (MeasureTheory.spanningSets μ i)) s = μ sAuxiliary lemma for iSup_restrict_spanningSets.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasureTheory.SigmaFinite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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 · cited by 9,879
- MeasurableSetstatement and proof · cited by 3,075
- iSupstatement · cited by 2,415
- MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
- MeasureTheory.SigmaFinitestatement and proof · cited by 526
- MeasureTheory.Measure.restrict_univproof · cited by 76
- MeasureTheory.spanningSetsstatement · cited by 45
- Monotone.directed_leproof · cited by 25
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.iSup_restrict_spanningSetsproof · cited by 2