\begin{definition}[Definition:General Euclidean Metric]
Let $\R^n$ be an $n$-dimensional real vector space.
The '''general Euclidean metrics''' are defined on $\R^n$ for $p \in \R_{\ge 1}$ as:
:$\ds \map {d_p} {x, y} := \paren {\sum_{i \mathop = 1}^n \size {x_i - y_i}^p}^{\frac 1 p}$
where $x = \tuple {x_1, x_2, \ldots, x_n}, y = \tuple {y_1, y_2, \ldots, y_n} \in \R^n$.
That is, they are the $p$-product metrics on $\R^n$.
\end{definition}