$ f:\mathcal{F} \to \mathbb{R} $ A **set function** $f$ is a function $:\mathcal{F} \to \mathbb{R}$, where $\mathcal{F}$ is a collection of subsets of a set $\mathcal{S}$. --- > [!example]- Probability is a set function. {💡 Example} > A **probability function** assigns a real number between 0 and 1 to [[Event|Events]] (sets of outcomes). > > For example, when rolling a die, the probability of an even number is $P(\{2,4,6\}) = 0.5$ > > We can assign a probability to any event in the Sample Space $S=\{1, 2, 3, 4, 5, 6\}$