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What is the concentration of the measure(c.o.m.)?

I am struggling with the following sentence;

"The phenomenon of the concentration of the measure for spheres in dimensions larger than 2."

I tried to figure it out about what the c.o.m. is, but I found only mathmetically rigorous explanations that I can't understand.

Please explain what it is. Even better if you have some intuitive examples. Thank you.

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You find a discussion of it in Yuri Manin: Mathematics and Physics, Birkhäuser.

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  • $\begingroup$ It seems a very interesting book and I do not mind reading it completely, but still - could you please indicate more specifically the place and context in which it is discussed? I believe this would make your answer much more helpful. I found some related explanations at the very beginning, explaining difficulties with the infinite-dimensional integration, is there something more in the text? $\endgroup$ – მამუკა ჯიბლაძე Aug 24 '16 at 7:43
  • $\begingroup$ I do not have the book with me now, and it is many years since I read it. But the book is very short so that you can find the relevant part easily. $\endgroup$ – Martin Peters Aug 24 '16 at 7:59
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    $\begingroup$ @MartinPeters 99 pages, according to dx.doi.org/10.1007/978-1-4899-6782-4 A chapter would be nice to cut it down somewhat. $\endgroup$ – David Roberts Aug 24 '16 at 8:52
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    $\begingroup$ Okay, I could check it now: pp 15 to 17. $\endgroup$ – Martin Peters Aug 24 '16 at 9:25

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