对一个引理的证明的商榷

A Discussion on the Proof of a Lemma

我们认为([1],page 22,Lemma2.1(b))的结论是对的,但证明过程有误。本文提出了修改意见。下面先简要说一下概念和符号: 在R^n中,非空子集U的直径用|U|表示。 (a)E(?)R^n,s≥0,(?)δ>0。

The equation{x: D^s(E, X)<a}=(?)F_p. plays an important role in the proof'of Lemma 2.1 in [1], but it does not hold in general. In this paper, we give two examples, to illustrate that, and give a correction of the proof.Let N=min{n: 1/n<a}and letF_(p,a-1/n)={x:(?)~s(E∩B_r(x))<(a-1/n)(2r)~s for some r<p} for n>N,then{x:D^s(E, x)<a}=(?)F_(p. a-1/n)