Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

a) A sequence of functions which is unbounded is neither point-wise nor uniformly convergent?

b) In case the sequence of functions is bounded below but unbounded above, or it is unbounded below but bounded above, the sequence of functions will be point-wise/uniformly convergent or not?

Please, explain!

share|improve this question
add comment

1 Answer

The sequence $\{f_n\}$ given by $f_n(x)=n\chi_{(0,n^{-1})}$ is below bounded but not above, and $f_n(x)\to 0$ for all $x$, so we can have pointwise convergence.

So we can't give an affirmation about pointwise convergence or not.

share|improve this answer
add comment

Your Answer

 
discard

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.