Chapter 16
Elements of Probability Theory
16.1. Measure spaces: probability spaces
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 ...
Get Mathematical Statistics and Stochastic Processes now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.