Theorems · Theorem · measure theory

MeasureTheory.Measure.ae_eq_image_of_ae_eq_comap

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} (f : α → β)
  (μ : MeasureTheory.Measure β),
  Function.Injective f →
    (∀ (s : Set α), MeasurableSet s → MeasureTheory.NullMeasurableSet (f '' s) μ) →
      ∀ {s t : Set α}, s =ᵐ[MeasureTheory.Measure.comap f μ] t → f '' s =ᵐ[μ] f '' t

Defined in: Mathlib.MeasureTheory.Measure.Comap
Cited by: 1 results in Mathlib
Foundations: Depth 193 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites16

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coeproof · 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
Set.ofPredproof · cited by 6,101
Set.imagestatement and proof · cited by 5,609
MeasurableSetstatement and proof · cited by 3,075
MeasureTheory.aestatement and proof · cited by 2,352
Set.extproof · cited by 2,266
Filter.EventuallyEqstatement and proof · cited by 1,912
MeasureTheory.NullMeasurableSetstatement and proof · cited by 337
MeasureTheory.Measure.comapstatement and proof · cited by 96

Cited by1

Results whose statement or proof uses this declaration.

MeasureTheory.Measure.NullMeasurableSet.imageproof · cited by 1