Measure Theory/Advanced set theory

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Structures of set theory[edit]

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 limits[edit]