 Solution

ID: past-exam-of-the-real-and-harmonic-analysis-course-of-the-university-of-oxford/2007/2/a/solution

X

μ : P (X) \to [0, \infty]

satisfying

μ (\emptyset) = 0

μ (⋃_{j} E_{j}) \leq \sum_{j} μ (E_{j}) .

M_{μ}^{*} = {A \subseteq X : μ (E) = μ (E \cap A) + μ (E ∖ A) for every E \subseteq X} .

The test runs over all subsets

E

, including nonmeasurable ones.

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