Mcshane积分与强Lusin条件

MCSHANE INTEGRATION AND STRONG LUSIN CONDITION

1972年J.Mcshane在KH-积分定义的基础上给以适当的限制,得出一种积分,人们称之为Mcshane积分(简记M-积分)。这种积分定义简单,不需引用测度,而且人们已经证明它与Lebesgue积分等价。从而,我们可以利用M-积分的特点,进一步刻划L-积分的性质。本文在高维空间中建立M-积分的两个定理;然后引入强Lusin条件概念。

In this paper we will research the properties on the Mcshane integral in R space by the step function; Then, We establish a Weak Equally Convergence Theorem by Strong Lusin's condition, and prove superiorty of the Weak Equally Convergence Theorem over the Lebesgue Control Convergence Theorem.