Intuitively, a metric outputs how different two things are, while a measure outputs how big something is.
In terms of inputs and outputs: a metric takes two points as input, and outputs a positive real number. A measure takes one set as input, and outputs a positive real number.
I think you might be confusing measures with metrics.
What’s the difference?
Intuitively, a metric outputs how different two things are, while a measure outputs how big something is.
In terms of inputs and outputs: a metric takes two points as input, and outputs a positive real number. A measure takes one set as input, and outputs a positive real number.
A metric gives the ‘distance’ between two points, while a measure gives the ‘weight’ of a subset (quotes are scare quotes).
Thanks…I’m just going to quietly retract the original comment.