Let $\mathbb{R}^N$ be a D5630: Set of euclidean real numbers.
Let $|\cdot| : \mathbb{R} \to [0, \infty)$ be the D412: Absolute value function.
The euclidean P-length function on $\mathbb{R}^N$ with respect to $p \in (0, \infty)$ is the D4365: Unsigned Realll func function \begin{equation} \Vert \cdot \Vert_p : \mathbb{R}^N \to [0, \infty), \quad \Vert x \Vert_p = \left( \sum_{n = 1}^N |x_n|^p \right)^{1 / p} \end{equation}