## The Zahorski theorem is valid in Gevrey classes

### Volume 151 / 1996

Fundamenta Mathematicae 151 (1996), 149-166
DOI: 10.4064/fm-151-2-149-166

#### Abstract

Let {Ω,F,G} be a partition of $ℝ^n$ such that Ω is open, F is $F_σ$ and of the first category, and G is $G_δ$. We prove that, for every γ ∈ ]1,∞[, there is an element of the Gevrey class Γγ which is analytic on Ω, has F as its set of defect points and has G as its set of divergence points.