A Generalization of a Theorem of Besicovitch
نویسنده
چکیده
In conclusion, I may point out that Theorem II may be generalized by a weakening of the hypothesis (d) . (1) In the first place, continuity of [a, g] f with respect to the pair of variables a, /3 may be replaced by upper semi-continuity . This generalization requires no change in the proof . (2) This continuity (or upper semi-continuity) with respect to (a, /3) is used only to show that the set A S is closed. A slight change in the proof shows that (d) may be replaced by (d') if a is fixed and 0 < a < a, then [a, g1f is an upper semicontinuous function of /3 in the range a < /3 < a .
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