平面上的近似连续积分

近似连续Ｐｅｒｒｏｎ 积分首先由Ｂｕｒｋｉｌｌ提出，称之为ＡＰ积分，由于近似复盖具有划分性质，因而可以给出ＡＰ积分的Ｒｉｅｍ ａｎｎ型定义． 但是，在平面上近似复盖是否具有划分性质还不知道． 本文给出了一种方法，用这种方法可以在平面上给出ＡＰ积分的Ｒｉｅｍ ａｎｎ型定义而不需要证明划分的存在性．

Approximately continuous integral in the plane

The approximately continuous Perron integral was first defined by Burkill using approximate limits in place of ordinary limits. It is also called the AP integral. A Riemann type definition of the AP integral was made possible in view of the fact that every approximate cover admits a partition. It is not known whether an approximate cover in the plane admits a partition. In this paper, we shall give an approach so that we may still define Riemann type definition of the AP integral in the plane without having to prove the existence of a partition from a given approximate cover in the plane.