Theorems · Theorem · probability

ProbabilityTheory.Kernel.densityProcess_fst_univ

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {mα : MeasurableSpace α} {mβ : MeasurableSpace β}
  {mγ : MeasurableSpace γ} [inst : MeasurableSpace.CountablyGenerated γ] {κ : ProbabilityTheory.Kernel α (γ × β)}
  [ProbabilityTheory.IsFiniteKernel κ] (n : ℕ) (a : α) (x : γ),
  κ.densityProcess κ.fst n a x Set.univ = if (κ.fst a) (MeasurableSpace.countablePartitionSet n x) = 0 then 0 else 1

Defined in

Mathlib.Probability.Kernel.Disintegration.Density

Cited by

1 results in Mathlib

Foundations

Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpace.CountablyGeneratedProbabilityTheory.IsFiniteKernel