Theorems · Theorem · probability

DependsOn.lmarginalPartialTraj_of_le

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

If f only depends on the variables up to rank a and a ≤ b, integrating f against partialTraj κ b c does nothing.

Defined in

Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj

Cited by

2 results in Mathlib

Foundations

Depth 233 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ProbabilityTheory.IsMarkovKernel