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Limit of simple functions

  1. Sep 26, 2013 #1
    http://www.proofwiki.org/wiki/Measurable_Function_Pointwise_Limit_of_Simple_Functions
    The following proof is shown in my book too. Basically it states that every measureable function can be written as the pointwise limit of a sequence of simple functions. Now, my problem is I don't see where the measureability of the limit-function is used crucially - so is the measureability really strictly necessary for the proof and if so where is it used? For me the statement might aswell be all functions can be written as the pointwise limit of a sequence of simple functions?
     
  2. jcsd
  3. Sep 26, 2013 #2

    Office_Shredder

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    If f was not measurable, then you wouldn't know that the fns were actually simple functions
     
    Last edited by a moderator: Sep 26, 2013
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