中文摘要：

在Banach空间X中利用序列的I-收敛与I＊-收敛给出理想J具可加性质（AP）的等价刻画，并进一步研究弱I-收敛、弱I＊-收敛、一致弱I＊-收敛之间，以及弱I-收敛与收敛之间的关系，最后基于I-λ-统计收敛给出其推广：I—A-统计收敛，并以次微分映射为工具定义一族有限可加测度，用于等价刻画I-A-统计收敛，这亦是有限可加测度的一个应用体现．

英文摘要：

Applying I-convergence and I＊-convergence of sequences in Banach space X, this paper first present a sufficient and neccessary condition for an ideal I has the ad- ditive property, then establish the relation between w-I-convergence, w-I＊-convergnence and uni-w-I＊-convergence, also the connection between w-I-convergence and Conver- gence, finally we define/-A-statistical convergence which is the generalization of I-A- statistical convergence, and by using subdifferential mapping to define a set of finite additive measures, we show the equivalent description of I-A-statistical convergence, this is an application of finite additive measures.