Theorems · Theorem · probability

ProbabilityTheory.Kernel.withDensity_kernel_sum

∀ {α : Type u_1} {β : Type u_2} {ι : Type u_3} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} [inst : Countable ι]
  (κ : ι → ProbabilityTheory.Kernel α β) (hκ : ∀ (i : ι), ProbabilityTheory.IsSFiniteKernel (κ i))
  (f : α → β → ENNReal),
  (ProbabilityTheory.Kernel.sum κ).withDensity f = ProbabilityTheory.Kernel.sum fun i => (κ i).withDensity f

Defined in

Mathlib.Probability.Kernel.WithDensity

Cited by

1 results in Mathlib

Foundations

Depth 211 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

Countable