Let $$\mu(A)=a \,\,\,\text{if}\,\,\,A=(-\infty,a] $$ $$\mu(A)=b-a \,\,\,\text{if}\,\,\,A=(a,b] $$ $$\mu(A)=-b \,\,\,\text{if}\,\,\,A=(b,\infty) $$ $$\mu(A)=0 \,\,\,\text{if}\,\,\,A=\mathbb R $$
This is an example given to us as an example of a finite but unbounded set function.
I know why it is finite but why is it unbounded?