Definition:P-Product Metric/Real Number Plane

Definition
Let $\R^2$ be the real number plane.

Let $p \in \R_{\ge 1}$.

The $p$-product metric on $\R^2$ is defined as:
 * $\displaystyle d_p \left({x, y}\right) := \sqrt [p] {\left\vert{x_1 - y_1}\right\vert^p + \left\vert{x_2 - y_2}\right\vert^p}$

where $x = \left({x_1, x_2}\right), y = \left({y_1, y_2}\right) \in \R^2$.

Also known as
The $p$-product metric is sometimes also referred to as the $r$-product metric by sources which use $r$ for the general power.

Some sources refer to this metric as the general (or generalized) Euclidean metric, and the space $\left({\R^2, d_p}\right)$ as the general (or generalized) Euclidean plane