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A Hypothesis on measurable sets

  1. Apr 3, 2017 #1
    Let ##D## be a bounded subset of ##\mathbb{R}^m##; equip the set ##2^D## with the Hausdorff distance. We have obtained a semimetric space. Turn this space into a metric space by the corresponding factorization. Denote this factor space by ##F##. Let ##\overline F## stand for comleteion of ##F##.

    Hypothesis. The standard Lebesgue ##\sigma-## algebra is an of first Baire category set in ##\overline F##.
    (The inclusion ##\sigma \subset \overline F## is understood in sense of corresponding embeddings)

    I tried to formalize an intuitive understanding (my understanding) that the set measurable subsets should be very small in the set of all subsets of ##\mathbb{R}^m##. Is that true what do you think?
     
  2. jcsd
  3. Apr 8, 2017 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
     
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