Theorems · Theorem · measure theory

MeasureTheory.Measure.restrict_pi_pi

∀ {ι : Type u_1} {α : ι → Type u_3} [inst : Fintype ι] [inst_1 : (i : ι) → MeasurableSpace (α i)]
  (μ : (i : ι) → MeasureTheory.Measure (α i)) [∀ (i : ι), MeasureTheory.SigmaFinite (μ i)] (s : (i : ι) → Set (α i)),
  (MeasureTheory.Measure.pi μ).restrict (Set.univ.pi fun i => s i) =
    MeasureTheory.Measure.pi fun i => (μ i).restrict (s i)

Defined in

Mathlib.MeasureTheory.Constructions.Pi

Cited by

2 results in Mathlib

Foundations

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

Assumes

FintypeMeasurableSpaceMeasureTheory.SigmaFinite