σ Algebra Notation
Contents
Sets and Subsets
The maximal set, which in probability applications is the sample space, is notated as Ω.
Subsets are usually named with calligraphic uppercase letters, but that's not exactly practical in typed notes. Capital letters will be used instead.
A subset of Ω is expressed as A ⊆ Ω.
Properties
The intersection of two sets is notated as A ⋂ B; the union of two sets is notated as A ⋃ B.
A pair of sets are disjoint if there is no intersection, which is expressed as A ⋂ B = ∅
Maps
Maps are usually named with blackboard bold letters, but that's not exactly practical in typed notes. Bold capital letters will be used instead.
A map translates a (sub)set into a real number. This can be expressed as P: Ω -> R.