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Mathematical Statistics and Stochastic Processes by Denis Bosq

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Chapter 16

Elements of Probability Theory

16.1. Measure spaces: probability spaces

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

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

1) images;

2) images;

3) images.

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

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

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

A probability ...

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