This result is stronger than what I quoted, it is for Borel Measurable Functions:

[Multilayer Feeforward Networks are Universal Approximators ](http://files.lossofgenerality.com/approx_hornik.pdf)

He does not use the word Neural for one reason that the feedforward networks could do the job for classical neural network definitions and some neural network variations might not satisfy the conditions for his theorem.

But for the same what we do his theorem is applicable.

Dara