Probability Measure

A probability measure on $S$ is a function $\text{Prob: }S\to [0,1]$ such that the sum of the values of the output of the function for each outcome is $1$; $\text{Prob}(s_1)+\text{Prob}(s_2)+\dots +\text{Prob}(s_n)=1$.

We can extend the probability measure to events: $\text{Prob: }\mathcal{P}(S)\to [0,1]$ such that the sum is once again $1$; $\text{Prob}(E)={\sum }_{s\in E}\text{Prob}(s)$.