 In order to take a conceptual viewpoint and to prove that V_t/K but not C_t/K can be approximated by superpositions of logistic functions on its domain of definition, we work on the theory of universal approximation on unbounded domains. We prove some general results which imply that an artificial neural network with a single hidden layer and sigmoid activation represents no function in L^{p(}%DIFDELCMD < \RR%%% ^2 \times 0, 1%DIFDELCMD < ]%%% ^{n neural network with a single hidden layer and logistic activation is a universal approximator of L^{2}( %DIFDELCMD < \RR %%%  \times [0, 1] ^{n^+ \times } [0, 1] ^{n .
<coherence>  In order to take a conceptual viewpoint and to prove that V_t/K but not C_t/K can be approximated by superpositions of logistic functions on its domain of definition, we work on the theory of universal approximation on unbounded domains. We prove some general results which imply that an artificial neural network with a single hidden layer and sigmoid activation represents no function in L^{p(}%DIFDELCMD < \RR%%% ^2 \times 0, 1%DIFDELCMD < ]%%% ^{n neural network with a single hidden layer and logistic activation is a universal approximator of L^{2}( %DIFDELCMD < \RR %%%  \times [0, 1] ^{n^+ \times } [0, 1] ^{n .
 (}%DIFDELCMD < \RR%%% ^2 \times 0, 1%DIFDELCMD < ]%%% ^{n neural network with a single hidden layer and logistic activation is a universal approximator of L^{2}( %DIFDELCMD < \RR %%% \times [0, 1] ^{n^+ \times } [0, 1] ^{n .