Definition:P-Product Metric/Real Vector Space
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Definition
Let $\R^n$ be an $n$-dimensional real vector space.
Let $p \in \R_{\ge 1}$.
The $p$-product metric on $\R^n$ is defined as:
- $\ds \map {d_p} {x, y} := \paren {\sum_{i \mathop = 1}^n \size {x_i - y_i}^p}^{\frac 1 p}$
where $x = \tuple {x_1, x_2, \ldots, x_n}, y = \tuple {y_1, y_2, \ldots, y_n} \in \R^n$.
Also see
Sources
- 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $2$: Continuity generalized: metric spaces: $2.2$: Examples: Example $2.2.18$