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pages/总复习2023t1.md

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 						  ![image.png](../assets/image_1686901196592_0.png)
 						- Property (iii) is called finite additivity.
 					- Axiomatic Definition of Probability ![section 1.4.pdf](../assets/section_1.4_1686901294123_0.pdf)
-						- A collection F of subsets of Ω is a σ-algebra if
+						- Let P (A)(A ∈ F ) be a non-negative set function on the σ-algebra
-						  (i) Ω ∈ F ;
+						  F . P (A) is called the probability measure or probability of
-						  (ii) F ∈ F =⇒ F ∈ F ;
+						  event A if it satisfies the following three axioms:
-						  (iii) if Fn is a countable collection of sets, n = 1, 2, · · · such that
+						  Axiom 1. for every A ∈ F , P (A) ⩾ 0;
-						  Fn ∈ F for all n, then
+						  Axiom 2. P (Ω) = 1;
-						- ![image.png](../assets/image_1686901503094_0.png)
+						  Axiom 3. (countable additivity) for every infinite sequence of
+						  countable disjoint events A1 , A2 , · · · ,
+						  ![image.png](../assets/image_1686901606535_0.png){:height 185, :width 405} 
+						  The sets in σ-algebra F are called events. F is called to be the
+						  algebra of events. ==The triple (Ω, F , P ) is a probability space
+						  or probability triple.==
+						- $$P (∅) = 0.$$
+						-
 					- Properties of Probability
 			- LATER 学积分
 			  :LOGBOOK: