Commit 2024-03-20 15:45 32531f6a
View on Github →feat: density of a finite kernel wrt another kernel (#10948)
Let κ : kernel α (γ × β)
and ν : kernel α γ
be two finite kernels with kernel.fst κ ≤ ν
, where γ
has a countably generated σ-algebra (true in particular for standard Borel spaces).
We build a function f : α → γ → Set β → ℝ
jointly measurable in the first two arguments such that for all a : α
and all measurable sets s : Set β
and A : Set γ
, ∫ x in A, f a x s ∂(ν a) = (κ a (A ×ˢ s)).toReal
.