Let $f : \mathbb{R}^n \to \mathbb{R}^m$ be a D4363: Euclidean real function such that

(i)	\begin{equation} f_{\mathsf{even}} : \mathbb{R}^n \to \mathbb{R}^m, \quad f_{\mathsf{even}}(x) = \frac{1}{2} ( f(x) + f(-x)) \end{equation}

Then $f_{\mathsf{even}}$ is an D3997: Even euclidean real function.