Convergence of abnormal integral

One 、 What is abnormal integral ？

1、 Integral with infinite integral interval or unbounded integrand , It is called abnormal integral （ Generalized integral ）
2、① Infinite anomalous integral ：

The interval can be pushed to [-∞,+∞];
② Unbounded anomalous integral ：

Be careful ！ Whether infinite integral or unbounded integral , All require their sub closed intervals to be Riemannian integrable .

Two 、 Convergence and divergence of anomalous integrals .

Others are similar to ;

3、 ... and 、p integral （ It plays a very important role in judging the convergence and divergence of other abnormal integrals ）

Four 、 An important characteristic of anomalous integral

The convergence and function limit of abnormal integral are 0 Or whether there is a bounded relationship ：
（1） Anomalous integral convergence “ Can't push out ” The limit of the function is 0 Contingent bounded
（2） The limit of the function is 0“ Can't push out ” Anomalous integral convergence

5、 ... and 、 Common topic