After our small excursion into measure theory, let us return to probability theory to study consequences of the results we have obtained in Chapter 1. A probability space is a triple (Ω, https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203742013/2214860d-c010-4236-82e7-9f319adfe56c/content/f.tif"/>, P) where Ω is a set, https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203742013/2214860d-c010-4236-82e7-9f319adfe56c/content/f.tif"/> is a σ-algebra and P is a probability measure on https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203742013/2214860d-c010-4236-82e7-9f319adfe56c/content/f.tif"/>, that is, (Ω, https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203742013/2214860d-c010-4236-82e7-9f319adfe56c/content/f.tif"/>, P) satisfies the following three axioms: