deterministic — Mathlib

English

Same conditional 0-1 tail law for atTop tail; conditional expectation of a tail set is almost surely 0 or 1.

Русский

Та же условная 0-1 хвостовая теорема для atTop; условное ожидание хвостового множества почти surely 0 или 1.

LaTeX

$$$\forall t\; ht\_tail \Rightarrow (\text{condExp } m μ\; (t.indicator) )\in \{0,1\} \text{ a.e.}$$$

Lean4

/-- Kernel which to `a` associates the dirac measure at `f a`. This is a Markov kernel. -/
noncomputable def deterministic (f : α → β) (hf : Measurable f) : Kernel α β
    where
  toFun a := Measure.dirac (f a)
  measurable' := by
    refine Measure.measurable_of_measurable_coe _ fun s hs => ?_
    simp_rw [Measure.dirac_apply' _ hs]
    exact measurable_one.indicator (hf hs)

Похожие утверждения