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

Meaning of vanishes outside a set of finite measure

  1. Nov 20, 2009 #1
    meaning of "vanishes outside a set of finite measure"

    What does it mean when we say that a function vanishes outside a set of finite measure? As in the definition of the integral as a prelude to the Lebesgue integral in Royden's Real Analysis, 3rd ed. (p. 77). It said:

    If [tex]\phi[/tex] vanishes outside a set of finite measure, we define the integral of [tex]\phi[/tex] by

    [tex]\int{\phi(x)dx} = \sum^{n}_{i=1}{{a_i}{mA_i}}[/tex]​
     
  2. jcsd
  3. Nov 20, 2009 #2
    Re: meaning of "vanishes outside a set of finite measure"

    it means [tex]\phi[/tex] is zero. think of the value of a characteristic function when x is outside the set of finite measure you're integrating over. hopefully i didn't embarrass myself this time :tongue2:
     
  4. Nov 20, 2009 #3

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Re: meaning of "vanishes outside a set of finite measure"

    It means there is a set E with finite measure such that f(x) = 0 if x is not in E.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Meaning of vanishes outside a set of finite measure
Loading...