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Date: 27-4-2021
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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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