Theorems · Theorem · probability

MeasureTheory.stronglyAdapted_iff_adapted

∀ {Ω : Type u_1} {ι : Type u_2} {m : MeasurableSpace Ω} [inst : Preorder ι] {f : MeasureTheory.Filtration ι m}
  {β : ι → Type u_3} [inst_1 : (i : ι) → TopologicalSpace (β i)] {u : (i : ι) → Ω → β i}
  [mΒ : (i : ι) → MeasurableSpace (β i)] [∀ (i : ι), BorelSpace (β i)]
  [∀ (i : ι), TopologicalSpace.PseudoMetrizableSpace (β i)] [∀ (i : ι), SecondCountableTopology (β i)],
  MeasureTheory.StronglyAdapted f u ↔ MeasureTheory.Adapted f u

Defined in

Mathlib.Probability.Process.Adapted

Cited by

0 results in Mathlib

Foundations

Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PreorderTopologicalSpaceMeasurableSpaceBorelSpaceTopologicalSpace.PseudoMetrizableSpaceSecondCountableTopology