Theorems · Theorem · measure theory

MeasureTheory.Measure.InnerRegularWRT.comap

∀ {α : Type u_2} {β : Type u_3} [inst : MeasurableSpace α] {mβ : MeasurableSpace β} {μ : MeasureTheory.Measure β}
  {pa qa : Set α → Prop} {pb qb : Set β → Prop},
  μ.InnerRegularWRT pb qb →
    ∀ {f : α → β},
      MeasurableEmbedding f →
        (∀ (U : Set α), qa U → qb (f '' U)) →
          (∀ K ⊆ Set.range f, pb K → pa (f ⁻¹' K)) → (MeasureTheory.Measure.comap f μ).InnerRegularWRT pa qa

Defined in

Mathlib.MeasureTheory.Measure.Regular

Cited by

2 results in Mathlib

Foundations

Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpace