一类广义二重积分

A Class of Generalized Double Integral

首先利用一个收敛级数构造了R上的一个特殊开集G，然后利用平面点集可求面积的充要条件，在平面上引入了一个有界的不可求面积的积分区域Ω，最后在Ω上定义了一个取正值的分段函数，并证明了其在Ω上的广义二重积分存在。

At first, a special open set G is constructed by using a convergent series. Then a bounded integration region Ω without area is introduced on the plane by using the necessary and sufficient conditions of plane point set with rectifiable area. Finally, a piecewise function achieving positive valued is defined on Ω,of which the existence of generalized double integral on Ω is proved.