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....0 or 1. Indeed, suppose on the contrary that 0 m(F ) 1. Since m(P (f) 0, it suces to show that m(F n P (f) 0: Denote by Z the set of all points z 2 F n P (f) such that m(B(z; r) F n P (f) 1: 2) In view of the Lebesgue density theorem (see for example Theorem 2.9. 11 in [7]) m(Z) m(F ) Since m(F ) 0 we nd at least one point z 2 Z. Since z 2 J(f)nP (f) there exists x 2 C nP (f) and an increasing sequence fn k g k=1 such that x = lim k 1 (z) and jf (z) xj =2 for every k 1, where = dist(x; P (f) 0. Suppose that m(B(x; nF ) 0. Obviously ....
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