What is the meaning of measure?

measure is a function that maps a set into the positive portion of the real line. Examples: 1. Length is a measure for subsets of the real line. Add the lengths of subsets of contiguous points in a set to get a positive real number. 2. Area is a measure for sets in the Cartesian plane. Take any rectangular set of points and compute its area by multiplying length by width to get a non negative real number. 3. Probability measure (q. V.).