Theorems · Theorem · measure theory
MeasureTheory.Measure.outerMeasure_le_iff
∀ {α : Type u_1} [inst : MeasurableSpace α] {μ : MeasureTheory.Measure α} {m : MeasureTheory.OuterMeasure α},
m ≤ μ.toOuterMeasure ↔ ∀ (s : Set α), MeasurableSet s → m s ≤ μ s- Cited by
- 3 results in Mathlib
- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- MeasureTheory.OuterMeasurestatement and proof · cited by 287
- MeasureTheory.Measure.toOuterMeasurestatement and proof · cited by 75
- MeasureTheory.Measure.trimmedproof · cited by 6
- MeasureTheory.OuterMeasure.le_trim_iffproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.le_iffproof · cited by 21
- MeasureTheory.measure_preimage_vadd_leproof · cited by 3
- MeasureTheory.measure_preimage_smul_leproof · cited by 3