Results on universal approximation for learners other than ANNs I have an applied machine-learning and statistics background, and when I read the Universal approximation theorem, which (in the context of the learning theory of ANNs - Artificial Neural Networks) states (Wikipedia): 


  "the standard multilayer feed-forward
  network with a single hidden layer
  that contains finite number of hidden
  neurons, and with arbitrary activation
  function are universal approximators
  on a compact subset of $R^n$. "


I wondered if there are any similar results (in terms of approximation power) for other types of learners (e.g. decision trees, boosting methods, SVMs, etc.). 

This leads me to a second but related question: Is this a topic that is formally studied in TCS? If so, are there any good texts for somebody with an applied background?

Thanks
Let me attempt to partly answer the learning part, or to at least address some connections.
In learning (distributional issues aside), we usually want our algorithms to be able to not only approximate the target function (from a class) with a hypothesis, but also to be able find such a hypothesis (efficiently).  So, even though a certain class can universally approximate a given target, we are not done.

I am not an expert in neural networks, but training a neural network is not easy.  We have algorithms for training a neural network, like backpropogation, but they won't always converge, or converge quickly enough, to meet the PAC learning criteria.
Boosting, on the other hand says (roughly) how to turn a weak "approximator" into a strong one, but it in some sense assumes the difficulty away but giving the learner access to the weak approximator.