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Obviously this change hasn’t happened. If this change is made, then it should be Haar integral, not Haar Integral.
These are some major edits. In general, it’s a good idea for the author making such major edits to document them here so that we can discuss them, rather than leaving it to others to hunt them down through red-and-green, which can be at times a chore.
For example, a decision was made to erase the positivity condition on Radon measures. Why was this done? Notice that in doing so, the definition of $\mu$ (“in the usual sense of measure theory”) as a certain supremum doesn’t seem quite right.
Not a huge change, but for some reason, Haar’s name is capitalized, but Hausdorff’s has been changed to lower-case. Why change an earlier author’s decision?
Is the lesser-known proof in the “Analogy” section documented somewhere? I think it’s an interesting question, just what is the dependence on choice principles in constructing Haar measures (it would be surprising to me if it were really needed, since uniqueness up to scalar multiple suggests a certain canonicity).
I’m not immediately tuning in to the remark on bar constructions, but maybe I haven’t thought hard enough. Are there also degeneracy maps floating around?
I may get in there at some point to prettify the formatting. Only in recent months have I begun to appreciate the considerable virtues of TikZ.
The article and its proofs are designed around the Haar integral instead of the Haar measure. This potentially more streamlined approach avoids heavy use of measure theory (or, I suppose one could say that it puts all the measure theory into the Riesz representation theorem). Considering this, I am attempting to rename the article Haar integral (last time it didn’t work for some reason).
added pointer to:
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