# Measure of the Mandelbrot Set

1. May 12, 2007

### Dragonfall

What is the Lebesgue measure of the Mandelbrot set?

2. May 16, 2007

### Dragonfall

Is it known?

3. May 16, 2007

### HallsofIvy

The mandelbrot set is not "Lebesque measurable". Is is possible that you are referring to the dimension of the set?

4. May 17, 2007

### LukeD

According to Wikipedia, the measure is estimated to be 1.506 591 77 ± 0.000 000 08, and it is conjectured to be exactly $$\sqrt{6\pi-1} - e$$

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
5. May 17, 2007

### Dragonfall

How do you know that it's not Lebesgue measurable?

6. Sep 3, 2009

### aquishix

<< insult deleted by Mentors >> every closed set is Lebesgue measurable.

The Mandelbrot Set is closed.

J

Last edited by a moderator: Sep 3, 2009
7. Sep 3, 2009

### aquishix

I know this is a very old post, but read what I just posted in reply.

J

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