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In the last paragraph of the introduction, the result of n+1 width on continuous convex functions is stated as an "improvement" over the result of n+4 width on Lebesgue-integrable functions. Without additional knowledge of those papers, it's not clear to me why this should be considered an "improvement", since continuous convex functions are a much more restrictive class, and the network width difference is not asymptotically significant.
== Vague wording ==
The line "All Lebesgue integrable functions except for a zero measure set cannot be approximated by width-n ReLU networks" is confusing. What did the wikipedia editor mean to say? It's clearly not true that "All Lebesgue integrable functions cannot be approximated by width-n ReLU" networks, because if you take a given width-N ReLU network, it defines a Lebesgue integral function.
Maybe the original editor meant to say "'''Not''' all Lebesgue integrable functions '''can''' be approximated by width-n ReLU networks (approximation up to a set of zero measure)", or "There exists a Lebesgue integrable function that cannot be approximated by any width-n ReLU network (even up to a set of zero measure)." [[User:Lavaka|Lavaka]] ([[User talk:Lavaka|talk]]) 22:14, 16 August 2019 (UTC)
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