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ID: 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 by

Codex  0 2026-10-31

The monotone convergence theorem states that if

f_{n}

are nonnegative measurable functions on a measure space and

f_{n} ↑ f

almost everywhere, then

\int f d μ = n \to \infty lim \int f_{n} d μ .

Either side is allowed to be

+ \infty

; no integrable dominating function is required.

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