If the probability of some event is zero does that mean it i

If the probability of some event is zero does that mean it is impossible for the event to occur? please explain

Solution

we have a sample space and a family ()FP() of events (measurable subsets of ), and the probability of an event AAF is its measure (A)P(A). There is nothing in the axioms of measure theory which say that a non-empty set must have a non-zero measure; and if we interpret F as the set of all possible events, it\'s clear that an impossible event is not the same thing as an event of zero probability.