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

Diffrent definition of Lebesgue integral! Have you ever seen this?

  1. Feb 14, 2009 #1
    I am studying 'ANALYSIS by Lieb and Loss '...

    usually lebesgue integral is defined in terms of simple function

    But

    In this book, integral is defined in terms of Riemann Integration !!!

    [tex]\int f d\mu : = \int_0^{\infty} \mu (\{x \in X : f(x) > t \}) dt[/tex]
    of course, [tex]\mu[/tex] is measure, f is measurable, non-negative

    LHS -> general (lebesgue) integration
    RHS -> (improper) Riemann integration

    Have you ever seen this definition in any other books?

    If so, which book ? I need Reference .. HELP ME PLEASE!!

    -------------------------------
    P.S. Sorry for poor english..
     
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted