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Let f1, . . . , fk be finitely many L1-functions on a measurable set E, and let d and r be numbers such that ∫E, fj, — d > r > 0 for all j. Then there is a measurable subset S of E such that ∫s fj = r for all j.
We construct an explicit continuous function F such that for each point x, every extended real number is a derived number of F at x and F has an infinite left and an infinite right derived number at x.
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