Theorems · Theorem · measure theory

MeasureTheory.measurePreserving_piFinsetUnion

∀ {ι : Type u_4} {α : ι → Type u_5} {x : (i : ι) → MeasurableSpace (α i)} [inst : DecidableEq ι] {s t : Finset ι}
  (h : Disjoint s t) (μ : (i : ι) → MeasureTheory.Measure (α i)) [∀ (i : ι), MeasureTheory.SigmaFinite (μ i)],
  MeasureTheory.MeasurePreserving (⇑(MeasurableEquiv.piFinsetUnion α h))
    ((MeasureTheory.Measure.pi fun i => μ ↑i).prod (MeasureTheory.Measure.pi fun i => μ ↑i))
    (MeasureTheory.Measure.pi fun i => μ ↑i)

Defined in

Mathlib.MeasureTheory.Constructions.Pi

Cited by

2 results in Mathlib

Foundations

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

Assumes

DecidableEqMeasureTheory.SigmaFinite