 Other examples of intervals are the set of numbers such that , the set of all of real numbers formula_1, the set of nonnegative real numbers, the set of positive real numbers, the empty set, and any singleton (set of one element).Real intervals play an important role in the theory of integration because they are the simplest sets whose "size" or "measure" or "length" is easy to define.The concept of measure can then be extended to more complicated sets of real numbers, leading to the Borel measure and eventually to the Lebesgue measure.