Theorems · Theorem · probability

MeasureTheory.measurable_inclusion_predictable

∀ {Ω : Type u_1} {ι : Type u_2} {m : MeasurableSpace Ω} [inst : LinearOrder ι] [inst_1 : OrderBot ι]
  [inst_2 : MeasurableSpace ι] [inst_3 : TopologicalSpace ι] [OpensMeasurableSpace ι] [OrderClosedTopology ι]
  {𝓕 : MeasureTheory.Filtration ι m} {i : ι}, Measurable fun x => (↑x.1, x.2)

The inclusion map from [0,i] × Ω with the subtype × 𝓕 i σ-algebra) to ι × Ω with the predictable σ-algebra is measurable

Defined in

Mathlib.Probability.Process.Predictable

Cited by

1 results in Mathlib

Foundations

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

Assumes

LinearOrderOrderBotMeasurableSpaceTopologicalSpaceOpensMeasurableSpaceOrderClosedTopology