Theorems · Theorem · measure theory

MeasureTheory.Measure.infinitePi_map_restrict

∀ {ι : Type u_1} {X : ι → Type u_2} {mX : (i : ι) → MeasurableSpace (X i)} (μ : (i : ι) → MeasureTheory.Measure (X i))
  [hμ : ∀ (i : ι), MeasureTheory.IsProbabilityMeasure (μ i)] {I : Finset ι},
  MeasureTheory.Measure.map I.restrict (MeasureTheory.Measure.infinitePi 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

5 results in Mathlib

Foundations

Depth 281 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasureTheory.IsProbabilityMeasure