多元积分中值定理的中间点(英文)

On the Intermediate Point of the Law of the Mean for Multiple Integral

研究了多元球体上的积分中值定理的中间点的渐近性质,证明了当球体半径趋于0时,中间点近似落在过球体中心的切平面上.

This paper is devoted to studying the asymptotical behavior of the intermediate point of the mean value theorem for integral on the balls with the fixed center. We show that the intermediate point of is asymptotically in the tangent hyperplane at the center of the ball when the radius of the balls approach O.