# 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 $\mathcal E$**.

### Discrete Sample Space

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

## Also see

- Definition:Elementary Event: a typical element of $\Omega$

## Sources

- 1986: Geoffrey Grimmett and Dominic Welsh:
*Probability: An Introduction*... (previous) ... (next): $\S 1.2$: Outcomes and events - 1986: Geoffrey Grimmett:
*Probability: An Introduction*: $\S 1.5$