What's it called when $g(x,y,z)$ can be expressed $g_x(x) + g_y(y) + g_z(z)$ for some function in $N$ dimensions in general?
I'm reading a paper and they seem to be calling this property "separable". But at least one definition of a separable function is: $g$ separable if $g(x,y,z) = g_x(x)g_y(y)g_z(z)$.
I call it completely additively separable functions as stated in wikipedia page of additively separable functions
Suppose $F$ is a function of $n$ variables $x_1, x_2, \ldots, x_n$. We say $F$ is completely additively separable if there exist functions $f_1, f_2, \ldots, f_n$, each a function of one variable, such that:
$$F(x_1, x_2, \ldots, x_n) = \sum_{i=1}^n f_i(x_i) $$
Notice that there is also a multiplicative version.
Suppose $G$ is a function of $n$ variables $x_1, x_2, \ldots, x_n$. We say $G$ is completely multiplicatively separable if there exist functions $g_1, g_2, \ldots, g_n$, each a function of one variable, such that:
$$G(x_1, x_2, \ldots, x_n) = \prod_{i=1}^n g_i(x_i) $$
