ABSTRACT
Modern probability theory takes its foundation in measure theory, and in this chapter we shall dip into the elementary part of this theory. Measure theory consists of two ingredients: sets of subsets, called pavings, and functions from sets of subsets into the real line R or the extended real line R ¯ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203742013/69a53f4e-97e6-48d7-bf94-69ab32e54fc6/content/eqn-in1_1.tif"/> called set functions. In the Introduction you have already encountered two kinds of pavings: algebras and σ-algebras. The characteristic of algebras and σ-algebras is that they are stable under certain set operations, such as complementation and finite or countable unions. We shall now formalize this stability notion.
