May 2012
Intermediate to advanced
304 pages
4h 44m
English
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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 ...
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