Could someone please direct me to a reference for the above proof (the one that does not use the axiom of choice)?
2026-03-27 01:54:20.1774576460
Henri Cartan's Proof of Existence and Uniqueness of Haar Measure
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Well, there's always Cartan's original paper
which you can find online at http://www.univie.ac.at/nuhag-php/bibtex/open_files/4197_ca400001.pdf. I don't know of a modern or English exposition of Cartan's original argument per se, but Alfsen gave a simplified version of Cartan's argument with a full exposition:
which you can find online at http://www.mscand.dk/article/view/10675/8696.