about its volume.
# The axioms of ZFC (Zermelo-Fraenkel set theory with the axiom of choice) might have to be altered.
# The volume of is or .

Standard measure theory takes the third option. One defines a family of measurable sets, which is very rich, and almost any set explicitly defined in most branches of mathematics will be among this family. It is usually very easy to prove that a given specific subset of the geometric plane is measurable. The fundamental assumption