Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Understanding the weak norm and it's notation

  1. Apr 5, 2012 #1

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

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

    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 [itex] \Big\{i \,|\, |x_i| > \epsilon \Big\} [/itex] mean?

    I found it in the context of a lecture for a class in compressive sensing:

    Thanks for any help you can provide.
  2. jcsd
  3. Apr 5, 2012 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

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

    For example, if [itex]\varepsilon=2[/itex] and


    Then the second, third and sixth element are [itex]>\varepsilon[/itex].
    So [itex]\{i~\vert~|x_i|>2\}=\{2,3,6\}[/itex].
  4. Apr 5, 2012 #3
    Thank you! That was nice and quick!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Understanding the weak norm and it's notation
  1. L2 - norm help (Replies: 2)

  2. Norm Limits (Replies: 1)