Erdős Problem #1126
PROVED LEANdatabase updated 2026-02-27
The statement as posed is true, and a proof exists. A solution has also been checked by machine, in Lean.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
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 \(x\). Proved independently by de Bruijn [dB66] and Jurkat [Ju65].
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/1126.Prizenone
Topicsanalysis
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/1126
Attempts
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