Theorems · Theorem · probability

ProbabilityTheory.Kernel.lmarginalPartialTraj_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))),
  b ≤ a → ∀ {f : ((n : ℕ) → X n) → ENNReal}, Measurable f → ProbabilityTheory.Kernel.lmarginalPartialTraj κ a b f = f

If b ≤ a, then integrating f against partialTraj κ a b does nothing.

Defined in

Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj

Cited by

4 results in Mathlib

Foundations

Depth 225 from the axioms · uses propext, Classical.choice, Quot.sound