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arXiv · 1209.4586

Almost orthogonally additive functions

Tomasz Kochanek·Wirginia Wyrobek-Kochanek
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Abstract

If a function $f$, acting on a Euclidean space $\mathbb{R}^n$, is "almost" orthogonally additive in the sense that $f(x+y)=f(x)+f(y)$ for all $(x,y)\in\bot\setminus Z$, where $Z$ is a "negligible" subset of the $(2n-1)$-dimensional manifold $\bot\subset\mathbb{R}^{2n}$, then $f$ coincides almost everywhere with some orthogonally additive mapping.

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Tomasz Kochanek, Wirginia Wyrobek-Kochanek. 2012-09-20. Almost orthogonally additive functions. https://arxiv.org/abs/1209.4586

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