Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

If $f_n$ -> f uniformly on every finite interval [a,b], does this imply it converges uniformly on R?

I would think yes, since R can be expressed as a sum of intervals...

share|cite|improve this question
up vote 1 down vote accepted

No. Consider the Taylor series for $e^x$ around $x=0$.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.