∀ {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 : ℕ) (x₀ : (i : ↥(Finset.Iic a)) → X ↑i),
  MeasureTheory.IsProjectiveLimit (ProbabilityTheory.Kernel.trajFun κ a x₀)
    (MeasureTheory.inducedFamily fun n => (ProbabilityTheory.Kernel.partialTraj κ a n) x₀)