Let $f_1, \dots, f_N : \mathbb{R}^K \to \mathbb{C}$ each be an D3997: Even euclidean real function such that

(i)	$\prod_{n = 1}^N f_n$ is the D4652: Pointwise function product of $f_1, \dots, f_N$

Then $\prod_{n = 1}^N f_n$ is an D3997: Even euclidean real function.