Multilayer Feedforward Networks Are Universal Approximators. Hornik, K., Stinchcombe, M., & White, H. 2(5):359–366.
Multilayer Feedforward Networks Are Universal Approximators [link]Paper  doi  abstract   bibtex   
This paper rigorously establishes that standard multilayer feedforward networks with as few as one hidden layer using arbitrary squashing functions are capable of approximating any Borel measurable function from one finite dimensional space to another to any desired degree of accuracy, provided sufficiently many hidden units are available. In this sense, multilayer feedforward networks are a class of universal approximators.
@article{hornikMultilayerFeedforwardNetworks1989,
  title = {Multilayer Feedforward Networks Are Universal Approximators},
  author = {Hornik, Kurt and Stinchcombe, Maxwell and White, Halbert},
  date = {1989-01},
  journaltitle = {Neural Networks},
  volume = {2},
  pages = {359--366},
  issn = {0893-6080},
  doi = {10.1016/0893-6080(89)90020-8},
  url = {https://doi.org/10.1016/0893-6080(89)90020-8},
  abstract = {This paper rigorously establishes that standard multilayer feedforward networks with as few as one hidden layer using arbitrary squashing functions are capable of approximating any Borel measurable function from one finite dimensional space to another to any desired degree of accuracy, provided sufficiently many hidden units are available. In this sense, multilayer feedforward networks are a class of universal approximators.},
  keywords = {*imported-from-citeulike-INRMM,~INRMM-MiD:c-1700245,artificial-neural-networks,back-propagation-networks,feedforward-networks,mapping-networks,network-representation-capability,sigma-pi-networks,squashing-functions,stone-weierstrass-theorem,universal-approximation},
  number = {5}
}
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