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Albertzeyer (talk | contribs) →Formal statement: ehm, i guess that was a typo? doesnt make sense otherwise |
Albertzeyer (talk | contribs) →Formal statement: cleanup (easier to read) |
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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>0</sub></sub> denote the ''m''<sub>0</sub>-dimensional unit hypercube [0,1]<sup>''m''<sub>0</sub></sup>. The space of continuous functions on ''I''<sub>''m''<sub>0</sub></sub> is denoted by ''C''(''I''<sub>''m''<sub>0</sub></sub>). Then, given any function ''f'' ∈ ''C''(''I''<sub>''m''<sub>0</sub></sub>) and є > 0, there exist an integer ''m''<sub>1</sub> and sets of real constants ''α''<sub>''i''</sub>, ''b''<sub>''i''</sub>
: <math>
F( x_1 , \dots, x_{m_0} ) =
\sum_{i=1}^{m_1} \alpha_i \varphi \left(
</math>
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