Theorems · Theorem · probability

MeasureTheory.Filtration.condExp_condExp

∀ {Ω : Type u_1} {ι : Type u_2} {m : MeasurableSpace Ω} [inst : Preorder ι] {E : Type u_3}
  [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace ℝ E] [CompleteSpace E] (f : Ω → E) {μ : MeasureTheory.Measure Ω}
  (ℱ : MeasureTheory.Filtration ι m) {i j : ι},
  i ≤ j → ∀ [MeasureTheory.SigmaFinite (μ.trim ⋯)], μ[μ[f | ↑ℱ j] | ↑ℱ i] =ᵐ[μ] μ[f | ↑ℱ i]

Defined in

Mathlib.Probability.Process.Filtration

Cited by

3 results in Mathlib

Foundations

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

Assumes

PreorderNormedAddCommGroupNormedSpaceCompleteSpaceMeasureTheory.SigmaFinite