Chapter 1 General Probability Theory 1 1 Infinite
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Chapter 1 General Probability Theory
1. 1 Infinite Probability Spaces • Finite • Infinite – Counterable (enumerate) – Uncounterable (real、無理數)
Cardinality
Definition 1. 1. 1 • Let be a nonempty set and let F be a collection of subsets of . We say that F is a -algebra provided that: (1) the empty set belongs to F (2) whenever a set A belongs to F, its complement also belongs to F (3) whenever a sequence of sets belongs to F, their union also belongs to F
Definition 1. 1. 2
Note
![Example 1. 1. 3 (Uniform (Lebesgue) measure on [0, 1])](http://slidetodoc.com/presentation_image_h2/d65f0bb66542b9a767a9cad2a4a29807/image-13.jpg "Example 1. 1. 3 (Uniform (Lebesgue) measure on [0, 1])")
Example 1. 1. 3 (Uniform (Lebesgue) measure on [0, 1])
Definition 1. 1. 5
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