Definition:Sample Space

Context
Probability Theory.

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.