Theorems · Theorem · probability

ProbabilityTheory.Kernel.isProjectiveMeasureFamily_partialTraj

∀ {X : ℕ → Type u_1} [inst : (n : ℕ) → MeasurableSpace (X n)]
  (κ : (n : ℕ) → ProbabilityTheory.Kernel ((i : ↥(Finset.Iic n)) → X ↑i) (X (n + 1)))
  [∀ (n : ℕ), ProbabilityTheory.IsMarkovKernel (κ n)] {a : ℕ} (x₀ : (i : ↥(Finset.Iic a)) → X ↑i),
  MeasureTheory.IsProjectiveMeasureFamily
    (MeasureTheory.inducedFamily fun b => (ProbabilityTheory.Kernel.partialTraj κ a b) x₀)

Defined in

Mathlib.Probability.Kernel.IonescuTulcea.Traj

Cited by

5 results in Mathlib

Foundations

Depth 233 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceProbabilityTheory.IsMarkovKernel