Theorems · Definition · measure theory
MeasureTheory.OuterMeasure.map
{α : Type u_1} → {β : Type u_3} → (α → β) → MeasureTheory.OuterMeasure α →ₗ[ENNReal] MeasureTheory.OuterMeasure βThe pushforward of m along f. The outer measure on s is defined to be m (f ⁻¹' s).
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- RingHom.idstatement · cited by 18,349
- LinearMapstatement · cited by 10,215
- ENNRealstatement · cited by 9,879
- Set.preimageproof · cited by 4,946
- Disjointproof · cited by 2,201
- Function.onFunproof · cited by 570
- Pairwiseproof · cited by 516
- MeasureTheory.OuterMeasurestatement and proof · cited by 287
- MeasureTheory.OuterMeasure.emptyproof · cited by 5
Cited by32
Results whose statement or proof uses this declaration.
- MeasureTheory.OuterMeasure.restrictproof · cited by 20
- MeasureTheory.Measure.mapₗproof · cited by 9
- MeasureTheory.Measure.map_apply₀proof · cited by 5
- MeasureTheory.OuterMeasure.map_applystatement · cited by 4
- MeasureTheory.Measure.mapₗ_congrproof · cited by 3
- MeasureTheory.OuterMeasure.map_comapstatement · cited by 2
- MeasureTheory.OuterMeasure.map_iInf_comapstatement and proof · cited by 2
- MeasureTheory.OuterMeasure.comap_mapstatement and proof · cited by 1
- MeasureTheory.OuterMeasure.restrict_iInfproof · cited by 1
- MeasureTheory.OuterMeasure.map_comap_lestatement · cited by 1
- MeasureTheory.OuterMeasure.map_comap_of_surjectivestatement · cited by 1
- MeasureTheory.OuterMeasure.map_iInfstatement and proof · cited by 1