Let Ω be a non-empty set and be the family of subsets of Ω.

DEFINITION 16.1.– is said to be a σ-algebra (or σ-field) on Ω if

1) ;

2) ;

3) .

Thus, and . The pair is called a measurable space.

In the following, if the An are pairwise disjoint, we will write Σn≥1 An for .

DEFINITION 16.2.– Let be a measurable space. A measure μ is a mapping from to such that and if where the An are pairwise disjoint,

A probability ...

Start Free Trial

No credit card required