超理想与二值有限可加测度

Ultraideals and two-valued finitely additive measures

  • 摘要: 讨论了超理想与二值有限可加测度的关系.从理想出发,研究了超理想的性质,得到了超理想的等价条件.一方面,以超理想为工具,构造了二值有限可加测度;另一方面,由一个二值有限可加测度得到了一个超理想.进而研究了两者的关系,证明了它们是一致的.

     

    Abstract: The main purpose of this paper is to show a kind of relation between ultraideals and two-valued finitely additive measures.Firstly,the properties of ultraideals are researched,and some equivalent conditions,that a ideal is ultraideals,are obtained.On the one hand,two-valued finitely additive measure is constructed with ultraideals;on the other hand,ultraideal is gotten with two-valued finitely additive measure.Furthermore,the consistence between them is proved.

     

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