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.
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.