Theorems · Theorem · probability

ProbabilityTheory.Kernel.iIndepFun.indepFun_sum_range_succ

∀ {α : Type u_1} {Ω : Type u_2} {mα : MeasurableSpace α} {mΩ : MeasurableSpace Ω} {κ : ProbabilityTheory.Kernel α Ω}
  {μ : MeasureTheory.Measure α} {β : Type u_8} {m : MeasurableSpace β} [inst : AddCommMonoid β] [MeasurableAdd₂ β]
  {f : ℕ → Ω → β},
  ProbabilityTheory.Kernel.iIndepFun f κ μ →
    (∀ (i : ℕ), Measurable (f i)) → ∀ (n : ℕ), ProbabilityTheory.Kernel.IndepFun (∑ j ∈ Finset.range n, f j) (f n) κ μ

Defined in

Mathlib.Probability.Independence.Kernel.IndepFun

Cited by

2 results in Mathlib

Foundations

Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidMeasurableAdd₂