Talk:Uniform boundedness

Examples?

This article is nice as far as it goes. It would be even better if there were examples of

1. A family which fails to have the property (e.g., fn(x) = x^(1/n)for x in (0.1, 1.0)

2. A family which has the property (e.g, sin(nx)).

Also, there should be words (or a link to) why this is a useful property. --anon

I put it on my to do list, which means I will get to it, but don't know when. If you would like to help, go ahead. :) Oleg Alexandrov (talk) 23:40, 2 December 2005 (UTC)

I finally got to it, more than a year late. :) Oleg Alexandrov (talk) 04:48, 26 January 2007 (UTC)

Sorry but i can't see why (1.) fails to have the property. |fn(x)| <= 1 forall n and for all x in (0.1,1.0). Didn't you mean an example for a family that isn't uniformly convergent instead of uniformly bounded? --SmH 19:59, 10 May 2006 (UTC)

I agree. However, take the example 2 above, and differentiate the functions. That yields an unbounded family. Oleg Alexandrov (talk) 04:48, 26 January 2007 (UTC)