Theorems · Theorem · measure theory

MeasureTheory.lintegral_eq_lmarginal_univ

∀ {δ : Type u_1} {X : δ → Type u_3} [inst : (i : δ) → MeasurableSpace (X i)] {μ : (i : δ) → MeasureTheory.Measure (X i)}
  [inst_1 : DecidableEq δ] [∀ (i : δ), MeasureTheory.SigmaFinite (μ i)] [inst_3 : Fintype δ]
  {f : ((i : δ) → X i) → ENNReal} (x : (i : δ) → X i),
  ∫⁻ (x : (i : δ) → X i), f x ∂MeasureTheory.Measure.pi μ = (∫⋯∫⁻_Finset.univ, f ∂μ) x

Defined in

Mathlib.MeasureTheory.Integral.Marginal

Cited by

3 results in Mathlib

Foundations

Depth 233 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceDecidableEqMeasureTheory.SigmaFiniteFintype