MeasurablySeparable — Mathlib

English

Two sets u and v in a measurable space are measurably separable if there exists a measurable set containing u and disjoint from v.

Русский

Две множества u и v в измеримом пространстве называются измеримо разделимыми, если существует измеримое множество, содержащее u и дискредитирующее v.

LaTeX

$$$\exists u, s \subseteq u \wedge Disjoint\ v\ u \wedge MeasurableSet\ u.$$$

Lean4

/-- Two sets `u` and `v` in a measurable space are measurably separable if there
exists a measurable set containing `u` and disjoint from `v`.
This is mostly interesting for Borel-separable sets. -/
def MeasurablySeparable {α : Type*} [MeasurableSpace α] (s t : Set α) : Prop :=
  ∃ u, s ⊆ u ∧ Disjoint t u ∧ MeasurableSet u

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