Theorems · Theorem · probability

DependsOn.lmarginalPartialTraj_const_right

∀ {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))}
  [∀ (n : ℕ), ProbabilityTheory.IsMarkovKernel (κ n)] {d : ℕ} {f : ((n : ℕ) → X n) → ENNReal},
  Measurable f →
    DependsOn f ↑(Finset.Iic a) →
      a ≤ c →
        a ≤ d →
          ProbabilityTheory.Kernel.lmarginalPartialTraj κ b c f = ProbabilityTheory.Kernel.lmarginalPartialTraj κ b d f

If f only depends on the variables uo to rank a, integrating beyond rank a is the same as integrating up to rank a.

Defined in

Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj

Cited by

1 results in Mathlib

Foundations

Depth 234 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ProbabilityTheory.IsMarkovKernel