Theorems · Theorem · measure theory

MeasureTheory.measurePreserving_piEquivPiSubtypeProd

∀ {ι : Type u_1} {α : ι → Type u_3} [inst : Fintype ι] {m : (i : ι) → MeasurableSpace (α i)}
  (μ : (i : ι) → MeasureTheory.Measure (α i)) [∀ (i : ι), MeasureTheory.SigmaFinite (μ i)] (p : ι → Prop)
  [inst_2 : DecidablePred p],
  MeasureTheory.MeasurePreserving (⇑(MeasurableEquiv.piEquivPiSubtypeProd α p)) (MeasureTheory.Measure.pi μ)
    ((MeasureTheory.Measure.pi fun i => μ ↑i).prod (MeasureTheory.Measure.pi fun i => μ ↑i))

Defined in

Mathlib.MeasureTheory.Constructions.Pi

Cited by

1 results in Mathlib

Foundations

Depth 231 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeMeasureTheory.SigmaFiniteDecidablePred