Theorems · Theorem · probability

MeasureTheory.Measure.dirac_compProd_apply

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {κ : ProbabilityTheory.Kernel α β}
  [MeasurableSingletonClass α] {a : α} [ProbabilityTheory.IsSFiniteKernel κ] {s : Set (α × β)},
  MeasurableSet s → ((MeasureTheory.Measure.dirac a).compProd κ) s = (κ a) (Prod.mk a ⁻¹' s)

Defined in

Mathlib.Probability.Kernel.Composition.MeasureCompProd

Cited by

1 results in Mathlib

Foundations

Depth 228 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSingletonClassProbabilityTheory.IsSFiniteKernel