Theorems · Theorem · measure theory

MeasureTheory.Measure.infinitePiNat_map_restrict

∀ {X : ℕ → Type u_1} {mX : (n : ℕ) → MeasurableSpace (X n)} (μ : (n : ℕ) → MeasureTheory.Measure (X n))
  [hμ : ∀ (n : ℕ), MeasureTheory.IsProbabilityMeasure (μ n)] (I : Finset ℕ),
  MeasureTheory.Measure.map I.restrict (MeasureTheory.Measure.infinitePiNat μ) = MeasureTheory.Measure.pi fun i => μ ↑i

Restricting the product measure to a product indexed by a finset yields the usual product measure.

Defined in

Mathlib.Probability.ProductMeasure

Cited by

2 results in Mathlib

Foundations

Depth 274 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasureTheory.IsProbabilityMeasure