Basic terms in probability theory are outcomes, sample space, events, and probability measure.

Outcomes and sample space . When you conduct a random experiment, there is a set of possible results of this experiment. This results are called outcomes. All possible outcomes together form a set, which is called sample space.

When one studies probability theory, a notion of a Borel $σ$-algebra arises. Here we will look at what this is. First thing is to understand what $σ$-algebra means. Let \(X\) be a set. Then if we have another set \(\mathcal B\), which we call σ-algebra over \(X\), if it has the following properties: it consists of subsets of \(X\), \(X \in \mathcal B\), for any \(b \in \mathcal B\), it follows that \(b^\C \in \mathcal B\), where superscript \(\C\) denotes complement,