First Baire class functions in the pluri-fine topology
| Autor: | Dovgoshey, Oleksiy, Küçükaslan, Mehmet, Riihentaus, Juhani |
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| Rok vydání: | 2015 |
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| Druh dokumentu: | Working Paper |
| Popis: | Let $B_{1}(\Omega, \mathbb R)$ be the first Baire class of real functions in the pluri-fine topology on an open set $\Omega \subseteq \mathbb C^{n}$ and let $H_{1}^{*}(\Omega, \mathbb R)$ be the first functional Lebesgue class of real functions in the same topology. We prove the equality $B_{1}(\Omega, \mathbb R)=H_{1}^{*}(\Omega, \mathbb R)$ and show that for every $f\in B_{1}(\Omega, \mathbb R)$ there is a separately continuous function $g: \Omega^{2} \to\mathbb R$ in the pluri-fine topology on $\Omega^2$ such that $f$ is the diagonal of $g.$ Comment: 10 pages |
| Databáze: | arXiv |
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