Definition:Event Space

Definition
Let $\mathcal E$ be an experiment.

The event space of $\mathcal E$ is usually denoted $\Sigma$ (Greek capital sigma), and is the set of all outcomes of $\mathcal E$ which are interesting.

Each of the elements of $\Sigma$ are elements of the power set of $\Omega$, and are called events.

Formal Definition
By definition, an experiment $\mathcal E$ has a probability space $\left({\Omega, \Sigma, \Pr}\right)$, which also by definition is a measure space.

Hence, again by definition, an event space $\Sigma$ is a sigma-algebra on $\Omega$.

Thus, an event space $\Sigma$ must fulfil the following requirements:

Also denoted as
Some sources use $\mathcal F$ or $\mathscr F$ to denote an event space.

In the field of decision theory, the symbol $\Xi$ can often be seen.

Also see

 * Elementary Properties of Event Space