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Hahn Decomposition Proof

  1. Dec 2, 2014 #1
    In the proof of the Hahn Decomposition Thm located here, there is the following sentence at the top of page 4.

    "However, we shall prove that there is a positive subset of E carrying a positive charge, thereby obtaining the
    contradiction."

    but, if ##G## is the positive subset of ##E## mentioned above then
    ##
    G \subset E\subset N
    ## which implies that ##N## is not a negative set. That seems to support the incorrect assumption, not contradict it. What am I missing?
     
  2. jcsd
  3. Dec 2, 2014 #2

    mathman

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    I haven't gone through the details, but I think it is trying to show that [itex]G\subset{P}[/itex] contradicting [itex]G\subset{N}[/itex].
     
  4. Dec 2, 2014 #3
    Yup. You're correct. Thanks, I was having a hard time with that one.
     
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