Theorems · Theorem · probability

ProbabilityTheory.Kernel.traj_map_frestrictLe_apply

∀ {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))}
  [inst_1 : ∀ (n : ℕ), ProbabilityTheory.IsMarkovKernel (κ n)] (a b : ℕ) (x : (i : ↥(Finset.Iic a)) → X ↑i),
  MeasureTheory.Measure.map (Preorder.frestrictLe b) ((ProbabilityTheory.Kernel.traj κ a) x) =
    (ProbabilityTheory.Kernel.partialTraj κ a b) x

Defined in

Mathlib.Probability.Kernel.IonescuTulcea.Traj

Cited by

0 results in Mathlib

Foundations

Depth 273 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceProbabilityTheory.IsMarkovKernel