Theorems · Theorem · measure theory

MeasurableEmbedding.map_comap

∀ {α : Type u_2} {β : Type u_3} {m0 : MeasurableSpace α} {m1 : MeasurableSpace β} {f : α → β},
  MeasurableEmbedding f →
    ∀ (μ : MeasureTheory.Measure β),
      MeasureTheory.Measure.map f (MeasureTheory.Measure.comap f μ) = μ.restrict (Set.range f)

Defined in: Mathlib.MeasureTheory.Measure.Restrict
Cited by: 8 results in Mathlib
Foundations: Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites19

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
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
ENNRealproof · cited by 9,879
Set.rangestatement and proof · cited by 4,705
MeasurableSetproof · cited by 3,075
MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
MeasureTheory.Measure.mapstatement · cited by 858
MeasureTheory.Measure.extproof · cited by 308
MeasurableEmbeddingstatement and proof · cited by 170
MeasureTheory.Measure.restrict_applyproof · cited by 159

Cited by8

Results whose statement or proof uses this declaration.

MeasurableEmbedding.comap_applyproof · cited by 20
map_comap_subtype_coeproof · cited by 14
Topology.IsClosedEmbedding.continuousOn_comap_finiteMeasureproof · cited by 1
MeasurableEmbedding.comap_preimageproof · cited by 1
MeasurableEmbedding.integrableAtFilter_iff_comapproof · cited by 1
MeasurableEmbedding.integrableOn_iff_comapproof · cited by 1
MeasurableSet.map_coe_volumeproof · cited by 0
UpperHalfPlane.volume_eq_lintegralproof · cited by 0