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Aug 14, 2015 at 19:58 comment added Michael Hardy So $\|f-g\|<\infty$ where $\|\cdot\|$ is the sup-norm. ${}\qquad{}$
Aug 14, 2015 at 8:41 comment added Jeremy Rickard By the way, I don't think $N$ plays any role in your condition.
Aug 14, 2015 at 4:40 history answered Robert Israel CC BY-SA 3.0