I don't think so, since the former is about the occurrence of sequences in stochastic, ergodic processes, and the latter is about approximating deterministic fu

I don't think so, since the former is about the occurrence of sequences in stochastic, ergodic processes, and the latter is about approximating deterministic functions. It's more like given an infinite number of parameters, you have enough degrees of freedom to describe the vector space a function lives in with some set of basis functions, and a neural net supplies that.