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Analysis Notation Question

  1. Nov 14, 2014 #1
    The context is Tonelli/Fubini.

    What's the difference between saying
    ##
    y\mapsto\int_Ef^y(x)dx
    ## is measurable
    and
    ##
    \int_Ef^y(x)dx
    ## is measurable
     
  2. jcsd
  3. Nov 14, 2014 #2

    mathman

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    There really isn't any. All the first statement is doing is emphasizing the fact that the integral is a measurable function of y.
     
  4. Nov 15, 2014 #3

    Fredrik

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    The second statement is a lazy version of the first. It's like saying that ##x^2## is differentiable instead of saying that ##x\mapsto x^2## is differentiable.
     
  5. Dec 2, 2014 #4
    OK thanks!
     
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