Theorems · Theorem · measure theory

MeasureTheory.integral_fintype_prod_volume_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)
  [inst_2 : (i : ι) → MeasureTheory.MeasureSpace (E i)] [∀ (i : ι), MeasureTheory.SigmaFinite MeasureTheory.volume],
  ∫ (x : (i : ι) → E i), ∏ i, f i (x i) = ∏ i, ∫ (x : E i), f i x

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

Defined in

Mathlib.MeasureTheory.Integral.Pi

Cited by

2 results in Mathlib

Foundations

Depth 269 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeRCLikeMeasureTheory.MeasureSpaceMeasureTheory.SigmaFinite