(An UAT with measure theory as foundation is essentially useless). Authors who blindly quote Cybenko/Hornik probably don't realise that is is as leaky as a sieve). It's a bit like the Weierstrass theorem .. warm feelings but is not constructive (in the precise sense of Errett Bishop).
https://en.wikipedia.org/wiki/Stone%E2% ... ss_theorem
Here's a related article UAT with again more 'sharpness'
https://arxiv.org/abs/2006.08859
Without metric spaces, Cauchy sequences, completeness and stuff like that, how is quantitative analysis possible?
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Till now determining optimal width and depth using class UAT as the holy grenade of Antioch is a bit ad hoc. Like getting a flat tire... solution is to drive around the block a few times, maybe it will fix itself.
www.youtube.com/watch?v=x91iciAYcw0