Our textbook states "The lenght l(I) of an interval I is defined to be the difference of the endpoints of I if I is bounded, and infinity if I is unbounded. Lenght is an example of a set function, that is, a function that assosiates an extended real number to each set in a collection of sets."
I'm having trouble understanding how a set function applies to length. For example, if we have an interval [-1,1], what is the extended real number? And what is the set that it is assosiated with?
Thanks in advance