6533b830fe1ef96bd1296557

RESEARCH PRODUCT

The Zahorski theorem is valid in Gevrey classes

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Let {Ω,F,G} be a partition of R such that Ω is open, F is Fσ and of the first category, and G is Gδ . 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.