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

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

    User Avatar
    Staff Emeritus
    Science Advisor

    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

    User Avatar
    Science Advisor
    Homework Helper
    2015 Award

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Lebesgue integral
  1. Lebesgue integral (Replies: 3)

  2. Lebesgue integration (Replies: 3)

  3. Lebesgue Integration (Replies: 3)

  4. Lebesgue integration (Replies: 2)

Loading...