Probability law $\mathbb{P}$

• A probability law is a function $\mathbb{P}:\mathcal{F} \rightarrow [0,1]$ of an event $E$ to a real number in $[0,1]$

• It is a measure of the size of a set. (Imagine it as the weight)

• Extends naturally to intervals $E= [a,b]$ is a subset of $\Omega = [0,1]$ for example and regions in higher dimensions.

$$\mathbb{P}[E] = \int_a^b f(x) dx \text{ where f(x) is the 'weight' for x.}$$