Theorems · Theorem · measure theory

MeasureTheory.MeasurePreserving.restrict_image_emb

∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β] {μa : MeasureTheory.Measure α}
  {μb : MeasureTheory.Measure β} {f : α → β},
  MeasureTheory.MeasurePreserving f μa μb →
    MeasurableEmbedding f → ∀ (s : Set α), MeasureTheory.MeasurePreserving f (μa.restrict s) (μb.restrict (f '' s))

Defined in

Mathlib.Dynamics.Ergodic.MeasurePreserving

Cited by

4 results in Mathlib

Foundations

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

Assumes

MeasurableSpaceMeasurableSpace