On the Convergence of Four Kinds of Relationship between the Sequence Functions

The paper used the elementary method to figure out the relationships between strong convergence,convergence in measure,almost everywhere convergence,and nearly uniform convergence.The conclusion is that the function must be the convergence in measure,but not vice versa.When the function sequence converges uniformly,it must be the almost everywhere convergence,but the converse is not true;there is no connection between strong convergence and almost everywhere convergence,neither is almost everywhere convergence and convergence in measure.