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.

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

In the book Weak convergence and Empirical Processes, by Aad W. van der Vaart and Jon A. Wellner, on page 81, the notation $l^\infty(\mathcal{F})$ appears, where $\mathcal{F}$ is a set of measurable functions, $f \in \mathcal{F}$ then $f \colon \mathcal{X} \rightarrow \mathbb{R}$.

I am not sure what $l^\infty(\mathcal{F})$ is. I know what $l^\infty$ is by itself, the set of bounded sequences (Wikipedia), but not sure about this one.

share|cite|improve this question
    
Will you please give a precise reference to where this is used? – Jonas Meyer Nov 12 '10 at 23:32
    
"Weak convergence and Empirical Processes", Aad W. van der Vaart Jon A. Wellner, page 81 (2.1). Thanks. – normvector Nov 12 '10 at 23:36
    
Thanks for the reference. Here's a link to Google Books for those interested: books.google.com/… – Jonas Meyer Nov 12 '10 at 23:47
1  
I'm not 100% sure, but the fact that $\mathcal{F}$ is mentioned as an "indexing set" suggests to me that it actually means just that: the everywhere bounded functions from $\mathcal{F}\to \mathbb{R}$. – Willie Wong Nov 13 '10 at 0:16
up vote 7 down vote accepted

Did you check page 34 (which I got by checking the List of Symbols on page 506)?

http://books.google.com/books?id=seH8dMrEgggC&pg=PA34

alt text

share|cite|improve this answer

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.