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Year 2 of the mathematics course of the University of Oxford

Options II course of the University of Oxford

Past exam of the options II course of the University of Oxford

2011

The <monotone convergence theorem> states that if $f_n$ are nonnegative <measurable function>[measurable functions] on a <measure space> and $f_n\uparrow f$ almost everywhere, then
$$
\boxed{\int f\,d\mu=\lim_{n\to\infty}\int f_n\,d\mu.}
$$
Either side is allowed to be $+\infty$; no integrable dominating function is required.

Solution

Past exam of the options II course of the University of Oxford / 2011 / D / D4 / a / Solution

Past exam of the options II course of the University of Oxford / 2011 / D / D4 / a / Solution

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Past exam of the options II course of the University of Oxford / 2011 / D / D4 / a / Solution

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