[see also: element, member, membership
Lebesgue discovered that a satisfactory theory of integration results if the sets Ei are allowed to belong to a larger class of subsets of the line.
Two consecutive elements do not belong both to A or both to B.
It turns out that A, B and C all belong to the same class, which we represent by the symbol P2.
For the sake of clarity, we shall indicate in what follows to which space X belongs.