Theorems · Theorem · probability

ProbabilityTheory.Kernel.IsProper.setLIntegral_eq_comp

∀ {X : Type u_1} {𝓑 𝓧 : MeasurableSpace X} {π : ProbabilityTheory.Kernel X X} {A B : Set X},
  π.IsProper →
    𝓑 ≤ 𝓧 →
      ∀ {μ : MeasureTheory.Measure X},
        MeasurableSet A → MeasurableSet B → ∫⁻ (a : X) in B, (π a) A ∂μ = (μ.bind ⇑π) (A ∩ B)

Defined in: Mathlib.Probability.Kernel.Proper
Cited by: 0 results in Mathlib
Foundations: Depth 212 from the axioms · uses propext, Classical.choice, Quot.sound

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