Definition:Sample Space

Definition
Let $\mathcal E$ be an experiment.

The sample space of $\mathcal E$ is usually denoted $\Omega$ (Greek capital omega), and is defined as the set of all possible outcomes of $\mathcal E$.

A typical element of $\Omega$ is called an elementary event and is often denoted by the symbol $\omega$ (Greek lowercase omega).

Discrete Sample Space
If $\Omega$ is a countable set, whether finite or infinite, then it is known as a discrete sample space.