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Problem related to signed measure

  1. Dec 3, 2008 #1
    1. The problem statement, all variables and given/known data
    (X,S,u) a measure space and f is in L1.
    Show that for any e>0, there exists a set E with u(E)<+infinity such that
    [tex]| \int_{E} fdu - \int_{X} fdu |<e [/tex]


    3. The attempt at a solution
    we can define a function
    [tex]v(A)=\int_{A}fdu [/tex]
    It is a well known result that v(A) is in fact a signed measure.

    We can somehow use the property of signed measures to show that there always exist a E such that |v(E)-v(X)|<e?
     
  2. jcsd
  3. Dec 3, 2008 #2

    morphism

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    Don't you need sigma-finiteness here or something of the sort?
     
  4. Dec 5, 2008 #3
    The question is as is, there is no mention of sigma finiteness. My attempt at the solution could be completely wrong.
     
  5. Dec 5, 2008 #4
    Let's suppose it is sigma finite? then what?
     
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