Stephen Dubin wrote:

>I often see (and use) the term "metric" as a particular kind of
>measure. However, I have had difficulty in finding a clear definition.
>This is made more difficult because of the more common use of
>"metric" as an adjective denoting the system of measurement units.
>Please tell me what I mean when I call something "a metric."

The word in that setting refers to a metric *function*, with the noun in 
the phrase left out; a common, if regrettable practise, seen in the use 
of words such as "professional" and "academic". A metric function on a 
suitable topology provides a measure analogous to distance.


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