Theorems · Theorem · measure theory
MeasureTheory.Measure.InnerRegularWRT.measure_eq_iSup
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {p q : Set α → Prop} {U : Set α},
μ.InnerRegularWRT p q → q U → μ U = ⨆ K, ⨆ (_ : K ⊆ U), ⨆ (_ : p K), μ K- Defined in
- Mathlib.MeasureTheory.Measure.Regular
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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 · cited by 2,415
- le_antisymmproof · cited by 2,068
- iSup_leproof · cited by 190
- iSup₂_leproof · cited by 96
- MeasureTheory.Measure.toOuterMeasureproof · cited by 75
- MeasureTheory.Measure.InnerRegularWRTstatement and proof · cited by 44
- MeasureTheory.OuterMeasure.monoproof · cited by 36
Cited by7
Results whose statement or proof uses this declaration.
- MeasurableSet.measure_eq_iSup_isCompactproof · cited by 4
- MeasurableSet.measure_eq_iSup_isCompact_of_ne_topproof · cited by 3
- IsOpen.measure_eq_iSup_isCompactproof · cited by 3
- MeasureTheory.Measure.InnerRegularWRT.smulproof · cited by 2
- MeasureTheory.Measure.InnerRegularWRT.eq_of_innerRegularWRT_of_forall_eqproof · cited by 1
- MeasurableSet.measure_eq_iSup_isClosed_of_ne_topproof · cited by 0
- IsOpen.measure_eq_iSup_isClosedproof · cited by 0