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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


    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
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