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In mathematics, a product metric is a metric on the Cartesian product of finitely many metric spaces , … , {\displaystyle ,\ldots ,} which metrizes the product topology. The most prominent product metrics are the p product metrics for a fixed p ∈ {\displaystyle p\in } :It is defined as the p norm of the n-vector of the distances measured in n subspaces:
For p = ∞ {\displaystyle p=\infty } this metric is also called the sup metric:
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