Theorems · Theorem · probability

ProbabilityTheory.IdentDistrib.integral_eq

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β]
  [inst_2 : MeasurableSpace γ] {μ : MeasureTheory.Measure α} {ν : MeasureTheory.Measure β} {f : α → γ} {g : β → γ}
  [inst_3 : NormedAddCommGroup γ] [inst_4 : NormedSpace ℝ γ] [BorelSpace γ],
  ProbabilityTheory.IdentDistrib f g μ ν → ∫ (x : α), f x ∂μ = ∫ (x : β), g x ∂ν

Defined in

Mathlib.Probability.IdentDistrib

Cited by

4 results in Mathlib

Foundations

Depth 255 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceMeasurableSpaceMeasurableSpaceNormedAddCommGroupNormedSpaceBorelSpace