论文标题
关于T-Normed积分在CMPACTA上的表征的一些评论
Some remarks on characterization of t-normed integrals on compacta
论文作者
论文摘要
对于有限的compacta，在\ cite {clm}中获得了t-norm的积分的表征，对于一般情况，在\ cite {rad}中获得了\ cite {rad}的表征。这样的表征建立了能力空间与均质尊重T-符号单调范围的功能之间的对应关系，从而保留了共酮函数的最大运行。实际上，我们可以将这些定理视为众所周知的Riesz定理的非添加和非线性类似物，内容涉及$σ$ - addive的常规孔测量和一组线性定义的函数之间的对应关系。我们讨论这种特征的最佳性。
A characterization of t-normed integrals was obtained in \cite{CLM} for finite compacta and in \cite{Rad} for the general case. Such characterization establishes a correspondence between the space of capacities and homogeneous respect t-norm monotone normed functionals preserving the maximum operation of comonotone functions. In fact these theorems we can consider as non-additive and non-linear analogues of well-known Riesz Theorem about a correspondence between the set of $σ$-additive regular Borel measures and the set of linear positively defined functionals. We discuss optimality of such characterization.
