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there are many versions of the theorem + a paper written by Cybenko does not prove that it is also called "Cybenko theorem" |
→Formal statement: simplifying the statement |
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<blockquote>
Let φ(·) be a nonconstant, bounded, and [[monotonic function|monotonically]]-increasing [[continuous function|continuous]] function. Let ''I''<sub>''m''</sub> denote the ''m''-dimensional unit hypercube [0,1]<sup>''m''</sup>. The space of continuous functions on ''I''<sub>''m''</sub> is denoted by ''C''(''I''<sub>''m''</sub>). Then, given any function ''f'' ∈ ''C''(''I''<sub>''m''</sub>) and є > 0, there exist an integer ''N'' and
: <math>
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