Theorems · Theorem · measure theory

MeasureTheory.isProjectiveMeasureFamily_pi

∀ {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)],
  MeasureTheory.IsProjectiveMeasureFamily fun I => MeasureTheory.Measure.pi fun i => μ ↑i

Consider a family of probability measures. You can take their products for any finite subfamily. This gives a projective family of measures.

Defined in

Mathlib.Probability.ProductMeasure

Cited by

4 results in Mathlib

Foundations

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

Assumes

MeasureTheory.IsProbabilityMeasure