Theorems · Theorem · probability

MeasureTheory.IsStronglyProgressive.finsetProd

∀ {Ω : Type u_1} {ι : Type u_2} {m : MeasurableSpace Ω} [inst : Preorder ι] {f : MeasureTheory.Filtration ι m}
  {β : Type u_3} [inst_1 : TopologicalSpace β] [inst_2 : MeasurableSpace ι] {γ : Type u_4} [inst_3 : CommMonoid β]
  [ContinuousMul β] {U : γ → ι → Ω → β} {s : Finset γ},
  (∀ c ∈ s, MeasureTheory.IsStronglyProgressive f (U c)) →
    MeasureTheory.IsStronglyProgressive f fun i a => ∏ c ∈ s, U c i a

Defined in

Mathlib.Probability.Process.Adapted

Cited by

2 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PreorderTopologicalSpaceMeasurableSpaceCommMonoidContinuousMul