Erdős Problem #1126

If\[f(x+y)=f(x)+f(y)\]for almost all $x,y\in \mathbb{R}$ then there exists a function $g$ such that\[g(x+y)=g(x)+g(y)\]for all $x,y\in\mathbb{R}$ such that $f(x)=g(x)$ for almost all $x$.

#1126: [Er60c]

analysis

Proved independently by de Bruijn [dB66] and Jurkat [Ju65].

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This page was last edited 30 December 2025.

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