Theorems · Theorem · probability

MeasureTheory.predictablePart_add

∀ {Ω : Type u_1} {E : Type u_2} {m0 : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} [inst : NormedAddCommGroup E]
  [inst_1 : NormedSpace ℝ E] {f g : ℕ → Ω → E} {ℱ : MeasureTheory.Filtration ℕ m0} [CompleteSpace E],
  (∀ (n : ℕ), MeasureTheory.Integrable (f n) μ) →
    (∀ (n : ℕ), MeasureTheory.Integrable (g n) μ) →
      ∀ (n : ℕ),
        MeasureTheory.predictablePart (f + g) ℱ μ n =ᵐ[μ]
          MeasureTheory.predictablePart f ℱ μ n + MeasureTheory.predictablePart g ℱ μ n

Defined in

Mathlib.Probability.Martingale.Centering

Cited by

1 results in Mathlib

Foundations

Depth 298 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceCompleteSpace