Theorems · Theorem · measure theory

ContinuousLinearMap.comp_condExp_comm

∀ {α : Type u_1} {E : Type u_3} {m m₀ : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : α → E}
  [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [CompleteSpace E] {F : Type u_5}
  [inst_3 : NormedAddCommGroup F] [CompleteSpace F] [inst_5 : NormedSpace ℝ F],
  MeasureTheory.Integrable f μ → ∀ (T : E →L[ℝ] F), ⇑T ∘ μ[f | m] =ᵐ[μ] μ[⇑T ∘ f | m]

Conditional expectation commutes with continuous linear maps.

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic

Cited by

2 results in Mathlib

Foundations

Depth 299 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceCompleteSpaceNormedAddCommGroupCompleteSpaceNormedSpace