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Metric derivative
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Metric derivative : ウィキペディア英語版
Metric derivative
In mathematics, the metric derivative is a notion of derivative appropriate to parametrized paths in metric spaces. It generalizes the notion of "speed" or "absolute velocity" to spaces which have a notion of distance (i.e. metric spaces) but not direction (such as vector spaces).
==Definition==

Let (M, d) be a metric space. Let E \subseteq \mathbb have a limit point at t \in \mathbb. Let \gamma : E \to M be a path. Then the metric derivative of \gamma at t, denoted | \gamma' | (t), is defined by
:| \gamma' | (t) := \lim_ \frac,
if this limit exists.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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