拉格朗日微分中值定理中间点集的稳定性

The Stability of Intermediate Value Point Set of Lagrange Mean Value Theorem for Differential

先给出拉格朗日微分中值定理本质中间点的定义,再研究其定理中间点集的稳定性,最后得到闭区间[a,b]上大多数一阶导函数都连续函数的中间点集在Baire分类意义下均为稳定的,并给出其中间点集为本质连通区的一个充分条件。

The concept of essential intermediate value point in lagrange mean value theorem for differential is in- troduced, and the stability of the intermediate value point set is discussed .It proves that the intermediate value point set of most the first-order derivative and continuous function （ in the Baire category sense） is stable ; and a sufficient condition for the existence of one essential component in the intermediate value point set of the first-or- der derivative and continuous function is obtain.