English
An analytic set is the continuous image of a Polish space; analytic sets form a robust class in descriptive set theory.
Русский
Аналитическое множество — непрерывное изображение полского пространства; класс аналитических множеств важен в теории описательных множеств.
LaTeX
$$$ \mathcal{A}(S) \text{ analytic } S $$$
Lean4
/-- An analytic set is a set which is the continuous image of some Polish space. There are several
equivalent characterizations of this definition. For the definition, we pick one that avoids
universe issues: a set is analytic if and only if it is a continuous image of `ℕ → ℕ` (or if it
is empty). The above more usual characterization is given
in `analyticSet_iff_exists_polishSpace_range`.
Warning: these are analytic sets in the context of descriptive set theory (which is why they are
registered in the namespace `MeasureTheory`). They have nothing to do with analytic sets in the
context of complex analysis. -/
def AnalyticSet :=
val_proj @wrapped✝.{}
