Theorems · Definition · measure theory

MeasureTheory.Measure.infinitePiNat

{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)] → MeasureTheory.Measure ((n : ℕ) → X n)

Infinite product measure indexed by ℕ. This is an auxiliary construction, you should use the generic product measure Measure.infinitePi.

Defined in

Mathlib.Probability.ProductMeasure

Cited by

5 results in Mathlib

Foundations

Depth 271 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasureTheory.IsProbabilityMeasure