摘要
设p、q是任意二正实数 ,则常义积分∫ba｜f(x) ｜pdx <+∞ ∫ba｜f(x)｜qdx <+∞。对于这个等价关系 ,无界函数的广义积分∫ba｜f(x) ｜dx和无穷级数 ∑∞i=1 ｜ui｜各自保留了彼此相反的一半的性质 ,而无穷限广义积分完全否定了这些性质。
Let p and q be two positive real numbers then,regular integral ∫ b a｜f(x)｜ p d x<+∞∫ b a｜f(x)｜ q d x<+∞ To this equiralent relation,improper integral of boundless function ∫ b a｜f(x)｜ d x and infinite series ∑∞i=1｜u i｜ retain half_properties respectively which are opposite to each other,where as,improper integral of infinite limit denies these properties completely.
基金
重庆市教委高等学校自然科学基金资助项目
