V2EX quasimetric

Quasimetric

释义 Definition

quasimetric(准度量/拟度量):一种类似“度量(metric)”的距离函数,但不一定满足对称性(即一般允许 \(d(x,y) \neq d(y,x)\))。在一些定义中,它仍满足非负性、同一性(\(d(x,x)=0\))、以及某种形式的三角不等式;不同学科对“quasimetric”的具体公理可能略有差异。

发音 Pronunciation (IPA)

/kwzimtrk/

例句 Examples

A quasimetric can measure how different two items are even if the order matters.
准度量可以在“顺序有影响”的情况下衡量两个事物有多不同。

In some models of directed networks, a quasimetric captures travel cost where going from A to B is not the same as going from B to A.
在一些有向网络的模型中,准度量可以刻画出行成本:从 A 到 B 的代价不一定等于从 B 到 A 的代价。

词源 Etymology

quasi- 源自拉丁语,意为“仿佛、近似”;metric 来自希腊语 metron(“度量、尺度”)。合起来 quasimetric 字面就是“近似的度量”,强调它与标准“度量”相似,但会放宽某些条件(最常见的是放宽对称性)。

相关词 Related Words

文学与著作 Literary Works

  • R. Engelking, General Topology(通用拓扑学经典教材中讨论多种“类度量/广义距离”概念时会出现相关术语与框架)
  • S. Cobzas, Functional Analysis in Asymmetric Normed Spaces(不对称范数与相关距离结构中常用到 quasimetric 的思想与表述)
  • M. A. Deza & E. Deza, Encyclopedia of Distances(距离概念百科式著作,收录并比较多种“广义距离/准距离”结构)
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