Theorems · Theorem · measure theory
MeasureTheory.Measure.iSup_restrict_spanningSets
∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : MeasureTheory.SigmaFinite μ]
(s : Set α), ⨆ i, (μ.restrict (MeasureTheory.spanningSets μ i)) s = μ s- Cited by
- 2 results in Mathlib
- Foundations
- Depth 201 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.
Cites19
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
- iSupstatement and proof · cited by 2,415
- MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
- MeasureTheory.SigmaFinitestatement and proof · cited by 526
- MeasureTheory.SFiniteproof · cited by 449
- Set.inter_commproof · cited by 291
- MeasureTheory.Measure.restrict_applyproof · cited by 159
- MeasureTheory.toMeasurableproof · cited by 77
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.exists_subset_measure_lt_topproof · cited by 2
- MeasureTheory.measure_compl_sigmaFiniteSetWRTproof · cited by 1