2.7 AXIOMS OF PROBABILITY
The probability measure P of the probability space 
satisfies the following axioms:
- Axiom 1.
. - Axiom 2.
. - Axiom 3. For
and 
, where 
:
(2.44) 
All three axioms are consistent with intuition and the frequency interpretation of probability, as described in Chapter 1. Axiom 1 obviously states that the probability measure is nonnegative. Axiom 2 states that the probability of some event in 
occurring is 1: “something must happen.” From Axioms 1 and 2, the probability of any event in 
must lie in the range [0, 1]; events are assigned probabilities that do not exceed 1.
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