411 REFERENCE · Wikibooks
Measure Theory/Advanced set theory
Reference material by Wikibooks contributors. This retains its source identity and is not 411 news reporting.
Structures of set theory
We begin by recalling the basic notions of set theory, which should be familiar to everybody:
0 100% #FFFFFF 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:
0 100% #FFFFFF Theorem 1.2:
Let be a universal set. Let , the power set of .
Set-theoretic limits