 Solution

ID: past-exam-of-the-options-ii-course-of-the-university-of-oxford/2008-printed-variant/d/d3/a/i/solution

0 \leq f_{1} \leq f_{2} \leq \dots

and converge pointwise to

f

, then

f

is measurable and

\int f = n lim \int f_{n},

allowing the common value to be

+ \infty

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