Theorems · Theorem · probability

ProbabilityTheory.Kernel.IndepSets.indepSet_of_mem

∀ {α : Type u_1} {Ω : Type u_2} {_mα : MeasurableSpace α} {s t : Set Ω} (S T : Set (Set Ω)) {_m0 : MeasurableSpace Ω},
  s ∈ S →
    t ∈ T →
      MeasurableSet s →
        MeasurableSet t →
          ∀ (κ : ProbabilityTheory.Kernel α Ω) (μ : MeasureTheory.Measure α) [ProbabilityTheory.IsZeroOrMarkovKernel κ],
            ProbabilityTheory.Kernel.IndepSets S T κ μ → ProbabilityTheory.Kernel.IndepSet s t κ μ

Defined in

Mathlib.Probability.Independence.Kernel.Indep

Cited by

2 results in Mathlib

Foundations

Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ProbabilityTheory.IsZeroOrMarkovKernel