Theorems · Theorem · probability

ProbabilityTheory.Kernel.traj_map_updateFinset

∀ {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)] {n : ℕ} (x : (i : ↥(Finset.Iic n)) → X ↑i),
  MeasureTheory.Measure.map (fun x_1 => Function.updateFinset x_1 (Finset.Iic n) x)
      ((ProbabilityTheory.Kernel.traj κ n) x) =
    (ProbabilityTheory.Kernel.traj κ n) x

Defined in

Mathlib.Probability.Kernel.IonescuTulcea.Traj

Cited by

3 results in Mathlib

Foundations

Depth 274 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceProbabilityTheory.IsMarkovKernel