Category:Definitions/P-Product Metrics
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This category contains definitions related to $p$-product metrics.
Related results can be found in Category:P-Product Metrics.
Let $M_{1'} = \struct {A_{1'}, d_{1'} }$ and $M_{2'} = \struct {A_{2'}, d_{2'} }$ be metric spaces.
Let $A_{1'} \times A_{2'}$ be the cartesian product of $A_{1'}$ and $A_{2'}$.
Let $p \in \R_{\ge 1}$.
The $p$-product metric on $A_{1'} \times A_{2'}$ is defined as:
- $\map {d_p} {x, y} := \paren {\paren {\map {d_{1'} } {x_1, y_1} }^p + \paren {\map {d_{2'} } {x_2, y_2} }^p}^{1/p}$
where $x = \tuple {x_1, x_2}, y = \tuple {y_1, y_2} \in A_{1'} \times A_{2'}$.
The metric space $\MM_p := \struct {A_{1'} \times A_{2'}, d_p}$ is the $p$-product (space) of $M_{1'}$ and $M_{2'}$.
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Pages in category "Definitions/P-Product Metrics"
The following 6 pages are in this category, out of 6 total.