A measure is a unit of time in Western music, also known as the bar. It represents a regular grouping of beats?, as indicated in notation by the time signature.
In mathematics:
A measure is a function from a class of subsets of a set to the real numbers in the range [0,inf). It is defined so as to give some idea of the relative "bigness" of the set. The intuitive idea of a measure is that little sets will have small measures, while bigger sets will have big measures.
A function is a measure iff:
Usually, mathematics deals with measures which also satisfy
It is important to note that the axiom of choice implies that there is no measure on the set of all subsets of the real numbers which gives the right values to intervals.
There are several measures in common use: