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Probability space
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A probability space is a set S, together with a σ-algebra X on S and a measure P on that σ-algebra such that P(S) = 1.
The set S is called the sample space and the elements of X are called the events.
The measure P is called the probability measure, and P(E) is the probability of the event E.
The above is a compact form of stating the probability axioms.
Note that sets containing one element of S are not necessarily events.
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