## Probability Space

The sample space $\Omega$ is the set of all possible outcomes of an experiment. Points in $\omega \in \Omega$ are outcomes or realizations.

## Limit Superior and Inferior of a Sequence

Definition 2.5.1 Let $\{s_n\}$ be a sequence in $\mathbb{R}$. The limit superior of $\{s_n\}$, denoted as $\limsup_{n\to\infty}s_n$, is defined as