A <null set> has <Lebesgue outer measure> zero: for every $\varepsilon>0$ it can be covered by countably many open intervals with total length below $\varepsilon$. If $E_j$ are null, cover $E_j$ by intervals of total length below $\varepsilon2^{-j}$, for $j\geq1$. The <union> of all these covers is countable and covers $\bigcup_jE_j$ with total length below $\varepsilon$. As $\varepsilon$ is arbitrary, \b[the countable <union> is null].

Solution

Past exam of the options I course of the University of Oxford / 2008 / D / D1 / a / Solution

 Solution (source code)