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arXiv · 1512.07475

Diagonals of separately absolutely continuous mappings and their analogues

Olena Karlova·Volodymyr Mykhaylyuk·Oleksandr Sobchuk
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Abstract

We prove that, for an interval $X\subseteq \mathbb R$ and a normed space $Z$ diagonals of separately absolute continuous mappings $f:X^2\to Z$ are exactly such mappings \mbox{$g:X\to Z$} that there is a sequence $(g_n)_{n=1}^{\infty}$ of continuous mappings $g_n:X\to Z$ with $\lim\limits_{n\to\infty}g_n(x)=g(x)$ and \mbox{$\sum\limits_{n=1}^{\infty}\|g_{n+1}(x)-g_n(x)\|<\infty$} for every $x\in X$.

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Olena Karlova, Volodymyr Mykhaylyuk, Oleksandr Sobchuk. 2015-12-23. Diagonals of separately absolutely continuous mappings and their analogues. https://arxiv.org/abs/1512.07475

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