Theorems · Theorem · measure theory

MeasurableEmbedding.comap_preimage

∀ {α : Type u_2} {β : Type u_3} {m0 : MeasurableSpace α} {m1 : MeasurableSpace β} {f : α → β},
  MeasurableEmbedding f →
    ∀ (μ : MeasureTheory.Measure β) (s : Set β), (MeasureTheory.Measure.comap f μ) (f ⁻¹' s) = μ (s ∩ Set.range f)

Defined in: Mathlib.MeasureTheory.Measure.Restrict
Cited by: 1 results in Mathlib
Foundations: Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites13

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.preimagestatement · cited by 4,946
Set.rangestatement and proof · cited by 4,705
MeasurableEmbeddingstatement and proof · cited by 170
MeasureTheory.Measure.comapstatement and proof · cited by 96
MeasureTheory.Measure.restrict_apply'proof · cited by 32
MeasurableEmbedding.map_applyproof · cited by 16
MeasurableEmbedding.measurableSet_rangeproof · cited by 11

Cited by1

Results whose statement or proof uses this declaration.

MeasurableEmbedding.variation_mapproof · cited by 3