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Measure of the Mandelbrot Set

  1. May 12, 2007 #1
    What is the Lebesgue measure of the Mandelbrot set?
  2. jcsd
  3. May 16, 2007 #2
    Is it known?
  4. May 16, 2007 #3


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    The mandelbrot set is not "Lebesque measurable". Is is possible that you are referring to the dimension of the set?
  5. May 17, 2007 #4
    According to Wikipedia, the measure is estimated to be 1.506 591 77 ± 0.000 000 08, and it is conjectured to be exactly [tex]\sqrt{6\pi-1} - e[/tex]

    edit: But after reading the source... I'm really not sure if I would trust that too well. However, the two large areas of the Mandelbrot set each definitely have positive measures
    Last edited: May 17, 2007
  6. May 17, 2007 #5
    How do you know that it's not Lebesgue measurable?
  7. Sep 3, 2009 #6
    << insult deleted by Mentors >> every closed set is Lebesgue measurable.

    The Mandelbrot Set is closed.

    Last edited by a moderator: Sep 3, 2009
  8. Sep 3, 2009 #7
    I know this is a very old post, but read what I just posted in reply.

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