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A L^2(0,1) space function

  1. Feb 14, 2017 #1
    If some function is element of space ##L^2(0,1)## then
    [tex]\int^1_0|f(x)|^2dx< \infty[/tex]. What in the case when it is not so simple to calculate this integral. For example ##f(x)=x^{-1}(C_1+C_2 \ln x)##. How to find is it this function in ##L^2(0,1)## for some ##C_1,C_2##?
     
  2. jcsd
  3. Feb 14, 2017 #2

    mathman

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    It is never (other than both constants = 0). Integral diverges at x=0.
     
  4. Feb 26, 2017 #3
    Please help me to define Relation between Lebesgue Differentiation and Lebesgue integration?
     
  5. Feb 26, 2017 #4

    mathman

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    I have never seen the term Lebesgue differentiation. Lebesgue integration is a theory of integration based on measure theory.
     
  6. Feb 26, 2017 #5

    WWGD

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    This is not quite the same as Lebesgue differentiation, bit it is kind of close to it:

    https://en.wikipedia.org/wiki/Lebesgue's_density_theorem
     
  7. Mar 8, 2017 #6
  8. Mar 9, 2017 #7

    WWGD

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    Ah, yes, Hawkeye's link is clearly better, more direct than mine.
     
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