Measure Theory/Advanced set theory

Structures of set theoryEdit

We begin by recalling the basic notions of set theory, which should be familiar to everybody:

Definition 1.1:

Let   be subsets of some universal set  .

  • The union of   and   is  .
  • The intersection of   and   is  .
  • The sum of   and   is  .

We will follow the convention to denote the intersection of   and   just by juxtaposition:  .

Given a universal set  , the subsets of   have the algebraic structure of a ring:

Theorem 1.2:

Let   be a universal set. Let  , the power set of  .

Set-theoretic limitsEdit