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Measurable set proof

  1. Aug 26, 2014 #1
    1. The problem statement, all variables and given/known data

    Let ##E \subset \mathbb R^n## be a measurable set such that ##E=A \cup B## with ##|B|=0## (##B## is a null set). Show that ##A## is measurable.

    3. The attempt at a solution

    I know that given ##\epsilon##, there exists a ##\sigma##-elementary set ##H## such that ##E \subset H## and ##m_e(H-E)<\epsilon##. How can I construct a ##\sigma-##elementary set ##H'## such that ##m_e(H-A)<\epsilon##?. Any suggestions would be appreciated
     
    Last edited: Aug 27, 2014
  2. jcsd
  3. Aug 27, 2014 #2

    HallsofIvy

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    What does |B| mean? Is it the measure of B or is the cardinality of B (in which case B is empty so that E= A).

    In your last sentence do you not mean "How can I construct an elementary set H' such that [itex]m_e(H'- A)<\epsilon[/itex]"?
     
  4. Aug 27, 2014 #3
    Edited, thanks for the correction.
     
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