Category:Definitions/Fréchet Product Metric

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This category contains definitions related to Fréchet Product Metric.
Related results can be found in Category:Fréchet Product Metric.


Let $\R^\omega$ denote the countable-dimensional real Cartesian space.

Let:

$x := \family {x_i}_{i \mathop \in \N} = \tuple {x_0, x_1, x_2, \ldots}$

and:

$y := \family {y_i}_{i \mathop \in \N} = \tuple {y_0, y_1, y_2, \ldots}$

denote arbitrary elements of $\R^\omega$.


Let the distance function $d: \R^\omega \times \R^\omega \to \R$ be applied to $\R^\omega$ as:

$\forall x, y \in \R^\omega: \map d {x, y} = \displaystyle \sum_{i \mathop \in \N} \dfrac {2^{-i} \size {x_i - y_i} } {1 + \size {x_i - y_i} }$


The distance function $d$ is referred to as the Fréchet (product) metric.


The resulting metric space $\struct {\R^\omega, d}$ is then referred to as the Fréchet (metric) space.

Pages in category "Definitions/Fréchet Product Metric"

The following 2 pages are in this category, out of 2 total.