【摘要】 讨论基于普通加法和乘法的一般实值可测函数的泛积分。我们将沿用经典Lebesgue积分的定义方式,将非负可测函数的泛积分定义延拓到一般实值可测函数,即将实值可测函数分解成两个非负可测函数的差,并定义实值可测函数的泛积分为这两个非负可测函数的泛积分之差。我们将进一步研究一般可测函数的泛积分的基本性质并给出泛积分的控制收敛定理。更多还原

【Abstract】 In the paper,we discuss the pan-integral for generalized real-valued measurable functions. Similar to the definition of Lebesgue integral for real-valued measurable functions,we decompose a real-valued measurable function to be the difference of two non-negative measurable functions,and define the pan-integral to be the difference of two pan-integral for non-negative measurable functions. We will further show some properties of the pan-integral and present the dominated convergence theorem.更多还原