Theorems · Theorem · measure theory

MeasureTheory.integral_fintype_prod_eq_prod

∀ {𝕜 : Type u_1} {ι : Type u_2} [inst : Fintype ι] [inst_1 : RCLike 𝕜] {E : ι → Type u_3} (f : (i : ι) → E i → 𝕜)
  {mE : (i : ι) → MeasurableSpace (E i)} {μ : (i : ι) → MeasureTheory.Measure (E i)}
  [∀ (i : ι), MeasureTheory.SigmaFinite (μ i)],
  ∫ (x : (i : ι) → E i), ∏ i, f i (x i) ∂MeasureTheory.Measure.pi μ = ∏ i, ∫ (x : E i), f i x ∂μ i

A version of Fubini's theorem with the variables indexed by a general finite type.

Defined in

Mathlib.MeasureTheory.Integral.Pi

Cited by

4 results in Mathlib

Foundations

Depth 268 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeRCLikeMeasureTheory.SigmaFinite