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Erdős problem 907

Let f:R→Rf:\mathbb{R}\to \mathbb{R} be such that f(x+h)−f(x)f(x+h)-f(x) is continuous for every h>0h>0. Is it true that f=g+hf=g+h for some continuous gg and additive hh (i.e. h(x+y)=h(x)+h(y)h(x+y)=h(x)+h(y))?

No current result

No reviewed Result is current in Vela Mathematics Program. Retained source material is shown below.

Retained declaration

FormalConjectures/ErdosProblems/907.lean

Formal Conjectures

FormalConjectures/ErdosProblems/907.leanErdos907.erdos_9074 linesExact file
True ↔  ∀ (f : ℝ → ℝ),    (∀ (h : ℝ), 0 < h → Continuous fun x => f (x + h) - f x) →      ∃ g a, Continuous g ∧ (∀ (x y : ℝ), a (x + y) = a x + a y) ∧ f = g + a
SolvedProof has a holelean4external proof

The proof uses `sorry`: part of the argument is written but not proved. Lean accepts the file; it does not accept the theorem.

Proof manifests naming this Problem

  • Jayyhk Erdős Leanjayyhk:erdos:907
  • PLBY Lean proofsErdosProblems.Erdos907

Reported activity

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