Theorems · Inductive type · measure theory

MeasureTheory.MeasurePreserving

{α : Type u_1} →
  {β : Type u_2} →
    [inst : MeasurableSpace α] →
      [inst_1 : MeasurableSpace β] →
        (α → β) →
          autoParam (MeasureTheory.Measure α) MeasureTheory.MeasurePreserving._auto_1 →
            autoParam (MeasureTheory.Measure β) MeasureTheory.MeasurePreserving._auto_3 → Prop

f is a measure-preserving map w.r.t. measures μa and μb if f is measurable and map f μa = μb.

Defined in

Mathlib.Dynamics.Ergodic.MeasurePreserving

Cited by

259 results in Mathlib

Foundations

Depth 9 from the axioms, rests on 34 definitions · uses no axioms

Assumes

MeasurableSpaceMeasurableSpace