Let I (a, b) and let f I R be a (not necessarily continuous) function We say that f is ' 'locally bounded ' ' at c I if there exists (c) 0 such that f is bounded on I (c (c), c (c) Prove that if f is locally bounded at every point of I, then f is bounded on I ...

The hypothesis that f is locally boun ...

Let I := (a, b) and let f : I R be a (not necessarily continuous)

Question:

Let I := (a, b) and let f : I → R be a (not necessarily continuous) function. We say that f is ''locally bounded'' at c ∈ I if there exists δ(c) > 0 such that f is bounded on I ∩(c - δ(c), c + δ(c). Prove that if f is locally bounded at every point of I, then f is bounded on I.