# 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 .