\b[No.] On the real line, the disjoint bounded Borel sets $[n,n+1)$, $n\geq0$, each have assigned mass zero, while their union $[0,\infty)$ has assigned mass one. This contradicts <countable additivity>, so the set function is not a <Borel measure>.

Solution

Past exam of the mathematics course of the University of Cambridge / 2015 / ii / Paper 1 / 23J / c / Solution

 Solution (source code)