First Baire class functions in the pluri-fine topology

2015/10/05 by Oleksiy Dovgoshey, Dovgoshey, Oleksiy, Mehmet Küçükaslan +3
Mathematics · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Advanced Topology and Set Theory

paper · pdf · doi:10.48550/arxiv.1510.01086

Abstract

Let B₁(Ω, \mathbb R) be the first Baire class of real functions in the pluri-fine topology on an open set Ω⊆ \mathbb Cⁿ and let H₁^*(Ω, \mathbb R) be the first functional Lebesgue class of real functions in the same topology. We prove the equality B₁(Ω, \mathbb R)=H₁^*(Ω, \mathbb R) and show that for every f∈ B₁(Ω, \mathbb R) there is a separately continuous function g: Ω² →\mathbb R in the pluri-fine topology on Ω² such that f is the diagonal of g.

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