Probability Axioms
المؤلف:
Doob, J. L
المصدر:
The Development of Rigor in Mathematical Probability (1900-1950)." Amer. Math. Monthly 103
الجزء والصفحة:
...
21-2-2022
1494
Probability Axioms
Given an event 
in a sample space 
which is either finite with 
elements or countably infinite with 
elements, then we can write
and a quantity 
, called the probability of event 
, is defined such that
1. 
.
2. 
.
3. Additivity: 
, where 
and 
are mutually exclusive.
4. Countable additivity: 
for 
, 2, ..., 
where 
, 
, ... are mutually exclusive (i.e., 
).
REFERENCES
Doob, J. L. "The Development of Rigor in Mathematical Probability (1900-1950)." Amer. Math. Monthly 103, 586-595, 1996.
Papoulis, A. Probability, Random Variables, and Stochastic Processes, 2nd ed. New York: McGraw-Hill, pp. 26-28, 1984.
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