Theorems · Theorem · measure theory

MeasureTheory.integral_fintype_prod_eq_pow

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

Defined in: Mathlib.MeasureTheory.Integral.Pi
Cited by: 1 results in Mathlib
Foundations: Depth 269 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Fintype RCLike MeasureTheory.SigmaFinite

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Cites14

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Realstatement · cited by 25,697
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
Fintypestatement and proof · cited by 7,736
Finset.univstatement and proof · cited by 3,473
RCLikestatement and proof · cited by 2,829
Finset.prodstatement · cited by 2,356
Finset.cardproof · cited by 2,327
MeasureTheory.integralstatement and proof · cited by 1,779
Fintype.cardstatement and proof · cited by 1,386
MeasureTheory.SigmaFinitestatement and proof · cited by 526
Finset.prod_constproof · cited by 154

Cited by1

Results whose statement or proof uses this declaration.

MeasureTheory.integral_fintype_prod_volume_eq_powproof · cited by 3