Metric

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In mathematics, a metric or distance function is a function that
defines a distance between each pair of point elements of a set.

A set with a metric is called a metric space.[1]
A metric induces a topology on a set, but not all topologies can be generated by a metric.
A topological space whose topology can be described by a metric is called metrizable.

One important source of metrics in differential geometry are
metric tensors, bilinear forms that may be defined from
the tangent vectors of a differentiable manifold onto a scalar.
A metric tensor allows distances along curves to be determined
through integration, and thus determines a metric.

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In mathematics, a metric space is a set together with a metric on the set.
The metric is a function that defines a concept of distance between
any two members of the set, which are usually called points.

The metric satisfies a few simple properties. Informally:

the distance from A to B is zero if and only if A and B are the same point,

the distance between two distinct points is positive,

the distance from A to B is the same as the distance from B to A, and

the distance from A to B (directly) is less than or equal to the distance
from A to B via any third point C.

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Metrics are measures of quantitative assessment commonly used for
assessing, comparing, and tracking performance or production.

Generally, a group of metrics will typically be used to build a dashboard that
management or analysts review on a regular basis to maintain performance assessments,
opinions, and business strategies.

https://www.investopedia.com/terms/m/metrics.asp

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In mathematical physics,
a metric describes the arrangement of relative distances within a surface or volume,
usually measured by signals passing through the region –
essentially describing the intrinsic geometry of the region.

An acoustic metric will describe the signal-carrying properties characteristic of
a given particulate medium in acoustics, or in fluid dynamics.

Other descriptive names such as sonic metric are also sometimes used,
interchangeably.

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Metric Spaces course
https://www.youtube.com/watch?v=XDmFAo66CRM

Oxford Mathematics
ผู้ติดตาม 2.67 แสน คน
For the first time we are making a full Oxford Mathematics Undergraduate
lecture course available.
Ben Green's 2nd Year Metric Spaces course is the first half of the Metric Spaces
and Complex Analysis course.
This is the second of 11 videos.