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单词 Metric identification
释义

Metric identification

中文百科

伪度量 Pseudometric space

(重定向自Metric identification)

对于集X中任意元素x,y,若实值函数d: (X,X) \to R符合以下三个条件,称它为一个伪度量(pseudometric)。

  • d(x,x)=0
  • d(x,y)=d(y,x)
  • d(x,z) \le d(x,y) + d(y,z)

它和一般距离(度量)的定义的分别只在于伪度量容许对于相异的元素x,yd(x,y)=0

英语百科

Pseudometric space 伪度量

(重定向自Metric identification)

In mathematics, a pseudometric space or semi-metric space is a generalized metric space in which the distance between two distinct points can be zero. In the same way as every normed space is a metric space, every seminormed space is a pseudometric space. Because of this analogy the term semimetric space (which has a different meaning in topology) is sometimes used as a synonym, especially in functional analysis.

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更新时间:2025/6/22 14:07:15