TITLE: Is this a known question about the expression of a function on $\Bbb R^2$ as an infinite sum of products?
QUESTION [27 upvotes]: The question below was posted on Mathematics Stack Exchange. It received no answer, and I do not expect any direct answer to it here. However, the question seems to me a natural one. Thus I wonder whether it has been posed before and, if so, whether there is any history to it. The question is:
Is there any function $f:\Bbb R^2\to\Bbb R$ which has no representation in the following form?
$$f(x,y)=\sum_{n=1}^{\infty} g_n(x)h_n(y)\quad(x,y\in \Bbb R).$$As a candidate for such a function, I suggest $f(x,y)=\min\{x,y\}$.

REPLY [3 votes]: I think this is solved in Shelah's 675-th paper: http://shelah.logic.at/files/675.pdf