Theorems · Theorem · measure theory

MeasureTheory.integral_comp_eval

∀ {ι : Type u_2} [inst : Fintype ι] {X : ι → Type u_3} {mX : (i : ι) → MeasurableSpace (X i)}
  {μ : (i : ι) → MeasureTheory.Measure (X i)} {E : Type u_4} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace ℝ E]
  [∀ (i : ι), MeasureTheory.IsProbabilityMeasure (μ i)] {i : ι} {f : X i → E},
  MeasureTheory.AEStronglyMeasurable f (μ i) →
    ∫ (x : (i : ι) → X i), f (x i) ∂MeasureTheory.Measure.pi μ = ∫ (x : X i), f x ∂μ i

Defined in

Mathlib.MeasureTheory.Integral.Pi

Cited by

1 results in Mathlib

Foundations

Depth 255 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeNormedAddCommGroupNormedSpaceMeasureTheory.IsProbabilityMeasure