@Pete. Thanks for the observation. I have made an edit accordingly, removing the specific example and replacing with a general situation.

If you keep working with the Borel sigma algebra, you might encounter problematic examples. For instance, a Hamel basis of R over Q. You can so arrange it that it is contained within a measure zero perfect set, for instance the Cantor set. This has measure zero in Lebesgue measure, but is nonmeasurable in the Borel setup.

How will you go from the wikipedia version of Golod-Shafarevich to your claim?

Holomorphy, or meromorphy?

@Engelbrekt. There is a discussion about you in the meta. Please see. Too many engelbrekts.....

So the first proof of the Abel-Jacobi theorem is independent of Cauchy's theorem? I thought this theorem had an essential homological content, as seen from the isomorphism of an elliptic curve with its Jacobian.

Mumford avoids the Jacobian altogether. Lang's book is not very organized and uses the old language. But I suppose I will indeed find Albanese and Picard there. Thanks.

Duplicate user engelbrekt? mathoverflow.net/users/2098/engelbrekt

Also the footnote contains an original reference to something in Zahlentheorie in Hilbert's collected works.