Theorems · Theorem · probability

ProbabilityTheory.Kernel.sum_prodMkLeft

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {mα : MeasurableSpace α} {mβ : MeasurableSpace β}
  {mγ : MeasurableSpace γ} {ι : Type u_5} [inst : Countable ι] {κ : ι → ProbabilityTheory.Kernel α β},
  (ProbabilityTheory.Kernel.sum fun i => ProbabilityTheory.Kernel.prodMkLeft γ (κ i)) =
    ProbabilityTheory.Kernel.prodMkLeft γ (ProbabilityTheory.Kernel.sum κ)

Defined in

Mathlib.Probability.Kernel.Composition.MapComap

Cited by

1 results in Mathlib

Foundations

Depth 195 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

Countable