Theorems · Theorem · measure theory

MeasureTheory.integral_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)} [inst_1 : (i : ι) → NormedAddCommGroup (X i)]
  [inst_2 : (i : ι) → NormedSpace ℝ (X i)] [∀ (i : ι), MeasureTheory.IsProbabilityMeasure (μ i)] {i : ι}
  [OpensMeasurableSpace (X i)] [SecondCountableTopology (X i)],
  ∫ (x : (i : ι) → X i), x i ∂MeasureTheory.Measure.pi μ = ∫ (x : X i), x ∂μ i

Defined in

Mathlib.MeasureTheory.Integral.Pi

Cited by

1 results in Mathlib

Foundations

Depth 256 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeNormedAddCommGroupNormedSpaceMeasureTheory.IsProbabilityMeasureOpensMeasurableSpaceSecondCountableTopology