Consider a function $(X,\epsilon)\mapsto f(X,\epsilon)$ where
$X$ is a vector $K\times 1$ belonging to $\mathbb{R}^K$
$\epsilon$ is a vector $M\times 1$ belonging to $\mathbb{R}^M$
$f(X,\epsilon)\in \mathbb{R}$
I would like your help to explain in words the following assumption:
$$ (\star) \hspace{1cm} f(X,\epsilon)\equiv g(X)+v(\epsilon) $$ with $g: \mathbb{R}^K\rightarrow \mathbb{R}$ and $v: \mathbb{R}^M\rightarrow \mathbb{R}$.
Is it correct to say "It is assumed that $f$ is additively separable over $X$ and $\epsilon$"? I am not convinced about it. Do you have better suggestions?