Theorems · Theorem · measure theory
MeasurableEmbedding.map_apply
∀ {α : Type u_1} {β : Type u_2} {m0 : MeasurableSpace α} {m1 : MeasurableSpace β} {f : α → β},
MeasurableEmbedding f → ∀ (μ : MeasureTheory.Measure α) (s : Set β), (MeasureTheory.Measure.map f μ) s = μ (f ⁻¹' s)- Defined in
- Mathlib.MeasureTheory.Measure.Map
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites36
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
- Set.imageproof · cited by 5,609
- Set.preimagestatement and proof · cited by 4,946
- Set.rangeproof · cited by 4,705
- MeasurableSetproof · cited by 3,075
- Compl.complproof · cited by 2,925
- le_antisymmproof · cited by 2,068
- MeasureTheory.Measure.mapstatement · cited by 858
Cited by16
Results whose statement or proof uses this declaration.
- MeasurableEquiv.map_applyproof · cited by 26
- MeasurableEmbedding.comap_applyproof · cited by 20
- MeasurableEmbedding.map_comapproof · cited by 8
- MeasurableEmbedding.restrict_mapproof · cited by 7
- MeasurableEmbedding.ae_map_iffproof · cited by 6
- MeasurableEmbedding.sigmaFinite_mapproof · cited by 3
- MeasureTheory.MeasurePreserving.measure_preimage_embproof · cited by 3
- MeasurableEmbedding.mutuallySingular_mapproof · cited by 2
- MeasureTheory.Measure.measurePreserving_homeomorphUnitSphereProdproof · cited by 2
- MeasurableEmbedding.map_injectiveproof · cited by 1
- MeasurableEmbedding.map_withDensity_rnDerivproof · cited by 1
- MeasurableEmbedding.absolutelyContinuous_mapproof · cited by 1