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 $x$ .

Source: erdosproblems.com/1126

Analysis

Wiki page

Status

SolvedProved

An accepted solution exists. The statement is true.

PROVED (LEAN), on the site's label, which credits the result as proved independently by de Bruijn [dB66] and Jurkat [Ju65]; both proofs are recorded as accepted claims, de Bruijn's translation-difference proof and Jurkat's conull-sumset proof. The Lean part of the label refers to a public formalization of de Bruijn's argument, linked from his claim page; the corpus has not built it.

Problem 1126

Status

Proof claims

Discussion