Theorems · Theorem · measure theory

MeasureTheory.Measure.pi_map_piCongrLeft

∀ {ι : Type u_1} {ι' : Type u_2} [inst : Fintype ι] [inst_1 : Fintype ι'] (e : ι ≃ ι') {β : ι' → Type u_4}
  [inst_2 : (i : ι') → MeasurableSpace (β i)] (μ : (i : ι') → MeasureTheory.Measure (β i))
  [∀ (i : ι'), MeasureTheory.SigmaFinite (μ i)],
  MeasureTheory.Measure.map (⇑(MeasurableEquiv.piCongrLeft (fun i => β i) e))
      (MeasureTheory.Measure.pi fun i => μ (e i)) =
    MeasureTheory.Measure.pi μ

Defined in

Mathlib.MeasureTheory.Constructions.Pi

Cited by

3 results in Mathlib

Foundations

Depth 232 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeFintypeMeasurableSpaceMeasureTheory.SigmaFinite