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Lebesgue integral

  1. Dec 7, 2005 #1
    let be the Lebesgue integral with a meassure [tex]\mu[/tex] then if we call this integral..

    [tex]\int_{X}fd\mu=I [/tex]

    my questions are..how would you calculate the integral of f(x)=exp(x) from 1 to 10?..another question let be the lebesgue integral on the interval X=(0,t) would be true that:

    [tex](\frac{d}{dt}\int_{X}fd\mu=f(t) [/tex]?

    thanks...
     
    Last edited: Dec 7, 2005
  2. jcsd
  3. Dec 7, 2005 #2

    HallsofIvy

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    The same way you would a Riemann integral. If a function is Riemann integrable on an interval, then it is Lebesque integrable on that interval and the two integrals are the same.

    Except possibly on a set of measure 0, yes.
     
  4. Dec 7, 2005 #3

    mathwonk

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    you need some hypotheses of course, but if f is "summable" then it is the derivative a.e. of its indefinite integral. see pages 11 and 47, 48 of Riesz Nagy.
     
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