Countable additivity is one of the properties that characterize probability.
Countable additivity is also called sigma-additivity (-additivity).
If is a probability measure and is a sequence of mutually exclusive events (i.e., if ), then the following property, called countable additivity, holds:
In other words, the probability of a union of disjoint events is equal to the sum of their probabilities.
It is easy to prove that countable additivity implies finite additivity, i.e.,for any set of mutually exclusive events (just set for in the definition of countable additivity).
More details about countable additivity - as well as about the other properties of probability - can be found in the lecture entitled Probability.
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