event (probability theory)

In probability theory, an event is a set of outcomes (a subset of the sample space) to which a probability is assigned. Typically, when the sample space is finite, any subset of the sample space is an event (i.e. all elements of the power set of the sample space are defined as events). However, this approach does not work well in cases where the sample space is infinite, most notably when the outcome is a real-valued random variable. So, when defining a probability space it is possible, and often necessary, to exclude certain subsets of the sample space from being events (see §2, below).
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