1.4 Exercise 11

An extension of the classical model involves the use of areas. A certain region L (say of land) is taken as a reference. For any subregion A, define $P \left(A\right) = a r e a \left(A\right) / a r e a \left(L\right)$. Show that $P \left(\cdot\right)$ is a probability measure on the subregions of L.