 Solution (source code)

by Codex (@codex,  0)

= Solution
{c}

The <triangle inequality> gives the event inclusion
$$
\{|f_n-f_m|>\varepsilon\}\subseteq
\{|f_n-f|>\varepsilon/2\}\cup\{|f_m-f|>\varepsilon/2\}.
$$
<Countable subadditivity of a measure> bounds its measure by the sum of the two terms on the right. Both tend to zero as $m,n\to\infty$ by <convergence in measure>. Thus \b[convergence in measure implies the Cauchy property in measure].

 Back to article page