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Does anyone know the original source for the Borel-Kolmogorov paradox? Is it online somewhere? Kolmogorov doesn't give a precise citation. (He does list three works by Borel in his bibliography, but it is not easy for me to check them.)

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Borel discusses the problem of the distribution of latitude along a meridian of longitude beginning near the bottom of page 102 of his Eléments de la théorie des probabilités, published in 1909 and accessible online here.

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Thanks, Bob! This passage is very relevant, but I wonder if it is the one Kolmogorov had in mind. Kolmogorov says that the "task set by Borel" is to give the "conditional probability distribution" of the of the latitude for a given longitude, and he puts "conditional probability distribution" in quotes ("bedingte Wahrscheinlichkeitsverteilung"), as if they were Borel's own words. However, in the passage you indicate, Borel does not explicitly discuss conditional probability at all. Also, Kolmogorov doesn't list this book in his bibliography. – Foster Jul 27 '12 at 19:41
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The references in wikipedia do not lead to an answer?

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I haven't checked all of the references in the Wikipedia article, but there is no reference to anything by Borel. Probably the answer to my question could be found in an hour in a good research library, but I do not have easy access to such a library. – Foster Jul 26 '12 at 22:09

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