Theorems · Theorem · measure theory

MeasureTheory.MeasurePreserving.aeconst_comp

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β]
  [inst_2 : MeasurableSpace γ] {μa : MeasureTheory.Measure α} {μb : MeasureTheory.Measure β}
  [MeasurableSingletonClass γ] {f : α → β},
  MeasureTheory.MeasurePreserving f μa μb →
    ∀ {g : β → γ},
      MeasureTheory.NullMeasurable g μb →
        (Filter.EventuallyConst (g ∘ f) (MeasureTheory.ae μa) ↔ Filter.EventuallyConst g (MeasureTheory.ae μb))

Defined in

Mathlib.Dynamics.Ergodic.MeasurePreserving

Cited by

1 results in Mathlib

Foundations

Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceMeasurableSpaceMeasurableSpaceMeasurableSingletonClass