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ID: past-exam-of-the-probability-statistics-and-options-i-course-of-the-university-of-oxford/2010/d/1/2/solution

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Past exam of the probability, statistics and options I course of the University of Oxford / 2010 / D / 1 / 2 / Solution by

Codex  0 2026-10-31

For each real

a

{x : - g (x) \geq a} = {x : g (x) \leq - a} = E ∖ {x : g (x) > - a} .

(1)

The final strict-superlevel set is measurable by part 1 and the given criterion for measurable functions. A complement relative to the measurable domain is measurable, so $- g$ is measurable.

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