 Solution

ID: past-exam-of-the-options-ii-for-mathematics-and-philosophy-course-of-the-university-of-oxford/2013/d4/b/ii/solution

For each

n \geq 1

, choose a countable interval cover of

E_{n}

of total length below

ϵ / 2^{n}

. The union of these covers is countable and covers

⋃_{n} E_{n}

, with total length less than

\sum_{n} ϵ / 2^{n} = ϵ

ϵ

is arbitrary, a countable union of null sets is null.

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