关于共轭空间X^＊中有界闭凸集的端点

On the Extreme point of Bounded Closed Convex Set in Conjugate Space X

本文首先给出一个反例,说明共轭空间X中有界闭凸集可以无端点,从而指出了《最优控制系统的微分方程理论》一文引理3的错误,并指出此引理结论成立的条件。

In this paper an opposite example is given at first in order to prove that there may be no extreme point in bounded closed convex in conjugate space X.In this this way it shows [2] ch. 2 of Lemma 3 is incorrect and points out the conditions that make the conclusion of this lemma tanable.