Theorems · Definition · measure theory

MeasureTheory.AEEqFun.compMeasurePreserving

{α : Type u_1} →
  {β : Type u_2} →
    {γ : Type u_3} →
      [inst : MeasurableSpace α] →
        {μ : MeasureTheory.Measure α} →
          [inst_1 : TopologicalSpace γ] →
            [inst_2 : MeasurableSpace β] →
              {ν : MeasureTheory.Measure β} →
                (β →ₘ[ν] γ) → (f : α → β) → MeasureTheory.MeasurePreserving f μ ν → α →ₘ[μ] γ

Composition of an almost everywhere equal function and a quasi-measure-preserving function. This is an important special case of AEEqFun.compQuasiMeasurePreserving. We use a separate definition so that lemmas that need f to be measure preserving can be @[simp] lemmas.

Defined in

Mathlib.MeasureTheory.Function.AEEqFun

Cited by

15 results in Mathlib

Foundations

Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceMeasurableSpace