Theorems · Theorem · measure theory
MeasureTheory.le_toMeasure_apply
∀ {α : Type u_1} [ms : MeasurableSpace α] (m : MeasureTheory.OuterMeasure α) (h : ms ≤ m.caratheodory) (s : Set α),
m s ≤ (m.toMeasure h) s- Cited by
- 8 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement · cited by 10,939
- ENNRealstatement · cited by 9,879
- MeasureTheory.OuterMeasurestatement and proof · cited by 287
- MeasureTheory.OuterMeasure.caratheodorystatement and proof · cited by 37
- MeasureTheory.OuterMeasure.toMeasurestatement · cited by 11
- MeasureTheory.OuterMeasure.le_trimproof · cited by 6
Cited by8
Results whose statement or proof uses this declaration.
- MeasureTheory.le_trimproof · cited by 10
- MeasureTheory.Measure.le_sum_applyproof · cited by 5
- MeasureTheory.Measure.le_comap_applyproof · cited by 2
- MeasureTheory.Measure.le_dirac_applyproof · cited by 2
- MeasureTheory.toMeasure_apply₀proof · cited by 2
- PMF.toOuterMeasure_apply_le_toMeasure_applyproof · cited by 1
- MeasureTheory.Measure.le_liftLinear_applyproof · cited by 0
- MeasureTheory.OuterMeasure.toMeasure_eq_zeroproof · cited by 0