Theorems · Theorem · probability

ProbabilityTheory.Kernel.lmarginalPartialTraj_self

∀ {X : ℕ → Type u_1} {mX : (n : ℕ) → MeasurableSpace (X n)} {a b c : ℕ}
  {κ : (n : ℕ) → ProbabilityTheory.Kernel ((i : ↥(Finset.Iic n)) → X ↑i) (X (n + 1))},
  a ≤ b →
    b ≤ c →
      ∀ {f : ((n : ℕ) → X n) → ENNReal},
        Measurable f →
          ProbabilityTheory.Kernel.lmarginalPartialTraj κ a b (ProbabilityTheory.Kernel.lmarginalPartialTraj κ b c f) =
            ProbabilityTheory.Kernel.lmarginalPartialTraj κ a c f

Integrating f against partialTraj κ a b and then against partialTraj κ b c is the same as integrating f against partialTraj κ a c.

Defined in

Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj

Cited by

2 results in Mathlib

Foundations

Depth 231 from the axioms · uses propext, Classical.choice, Quot.sound