Limit function not lipschitz.

Question

Is there a sequence of functions that are all lipschitz and uniformly continuous that converge uniformly to f and f need not be lipschitz?

If it is Lipschits, then it is uniformly continuous. – Mhenni Benghorbal Feb 08 '14 at 21:22 — Mhenni Benghorbal, Feb 08 '14 at 21:22

score 5 · Answer 1 · answered Feb 08 '14 at 19:25

5

Yes. Let $f_n(x)=\min\{nx,\sqrt x\}$ on $[0,1]$

answered Feb 08 '14 at 19:25

Hagen von Eitzen

1 Answers1