Understanding the weak norm and it's notation

[PhillipKP]

Hello.

I'm trying to grasp the notation for the definition of something called the weak q-norm, defined as

\|x\|_{q,w}^q = \sup\limits_{\epsilon > 0} \epsilon^q \left| \Big\{i \,|\, |x_i| > \epsilon \Big\} \right|

I don't come from a pure math background so I've never seen this notation before but I was wondering if someone knew what the notation inside the "braces" mean:

Specifically what does \Big\{i \,|\, |x_i| > \epsilon \Big\} mean?

I found it in the context of a lecture for a class in compressive sensing:
http://theproofisinthepudding.wordpress.com/2012/01/12/lecture-2/#more-543

Thanks for any help you can provide.

 

[micromass]

It is the set of all elements i such that |x_i|>\varepsilon.

For example, if \varepsilon=2 and

x=(2,5,3,1,2,6)

Then the second, third and sixth element are >\varepsilon.
So \{i~\vert~|x_i|>2\}=\{2,3,6\}.

 

[PhillipKP]

Thank you! That was nice and quick!