Conversation started May 4, 2012 at 21:25.
Matt N.
Matt N.
May 4, 2012 21:25
Thanks for pointing this out, I hadn't seen this answer. Too cool! He gets plus one from me for using my favourite theorem.
leo
leo
@tb Yes. I already have a post that implies that the outer measure of an interval is its length. You have an answer in there as well
t.b.
t.b.
@leo I know :)
@MattN heh! I like the pimped nested intervals principle, too :)
Matt N.
Matt N.
@tb soulmates : )
leo
leo
see you! all
Matt N.
Matt N.
Byee!
t.b.
t.b.
May 4, 2012 21:31
Bye, leo
ymar
ymar
@DylanMoreland May I take a bit of your time?
t.b.
t.b.
@MattN I wish I'd be better at applying it, though. It's one of the hardest things for me to use properly.
Matt N.
Matt N.
@tb I've been meaning to post a question about it. I want to see demonstrations of its alleged power. Just haven't gotten around to writing up the question. The side effect I am hoping for is that I get an idea of how to apply it.
t.b.
t.b.
@MattN That'd be really nice. My favorite exercise is: if $f:(0,\infty) \to \mathbb{R}$ is continuous and $f(nx) \xrightarrow{n\to\infty} 0$ for all $x \in (0,\infty)$ then $f(x) \xrightarrow{x\to\infty} 0$.
Matt N.
Matt N.
@tb I know, you've told me once before : ) But I forgot about it, so thanks for saying it again : )
Peter Tamaroff
Peter Tamaroff
May 4, 2012 21:36
@tb What would the steps be? Or hints? It find it intuitively true, but I'd like to take a shot.
Matt N.
Matt N.
@PeterTamaroff Hint: use the Baire category theorem.
Peter Tamaroff
Peter Tamaroff
@MattN Oh... bummer. It is topology related?
Matt N.
Matt N.
@tb Unless you would like to post this as an answer I could include it in the question. (along with some other application I had in mind)
t.b.
t.b.
@MattN Sure, go ahead. You could link to Gowers's take on it, too, to save yourself some work. Another nice application is the uncountability of dimension of infinite-dimensional Banach spaces and of course the standard facts in basic Futile Attempts.
@PeterTamaroff Suppose that $f(x+n) \xrightarrow{n \to \infty} 0$ for all $x \in (0,\infty)$. Is the result still true?
Matt N.
Matt N.
@tb Thank you! I'll see. I don't want to save too much work because the process of writing the question is already intended to help me learn some things.
(exactly some of those standard facts)
t.b.
t.b.
May 4, 2012 21:41
@MattN But to answer more directly: feel free to include that one.
Matt N.
Matt N.
@tb I understood. "Sure, go ahead" is pretty direct. : )
t.b.
t.b.
@MattN Not too coherent today, am I? :/ I'm sure I've linked you to the Sokal thingie already.
(not directly linked to your query in that it avoids Baire for uniform boundedness)
 
Conversation ended May 4, 2012 at 21:43.