Weak order convergence of Riesz space-valued positive vector measures with applications

Riesz空间值正向量测度的弱阶收敛及其应用

基本信息

批准号：
15540162
负责人：
KAWABE Jun
金额：
$ 2.24万
依托单位：
SHINSHU UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2004
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540162/
关键词：
Riesz space-valued measures weak convergence of measures Riesz type representation theorem portmanteau theorem bilinear vector integration Borel product of vector measures compactness criterion uniform order tightness リース空間値測度ベクトル測度のボレル

项目摘要

1.The existence and uniqueness of the Borel injective tensor product and the validity of a Fubini-type theorem are shown for two Banach space-valued vector measures. Thanks to this result, the convolution of Banach algebra-valued vector measures on a topological semigroup is defined as the measure induced by their Borel injective tensor product and the semigroup operation. The joint weak continuity of Borel injective tensor products or convolutions of vector measures is also proved.2.It is shown that the injective tensor product of positive vector measures in certain Banach lattices is jointly continuous with respect to weak convergence of vector measures. Our approach to this problem is based on Bartle's bilinear vector integration theory.3.Prokhorov-LeCam's compactness criteria and Varadarajan's metrizability criterion are given for vector measures with values in Frechet spaces, semi-reflexive spaces, and semi-Montel spaces.4.Compactness and sequential compactness criterion are given … More for a set of vector measures on a complete separable metric space with values in a certain semi-Montel space. Among others it is shown that a set of such vector measures is uniformly bounded and uniformly tight if and only if the corresponding set of real measures is relatively sequentially compact with respect to the usual weak convergence of measures.5.The validity of a version of the Portmanteau Theorem is shown for Dedekind complete Riesz space-valued σ-measures. From the result one can recognize that not the norm but the order structure on the space where vector measures take values is essential to the validity of the Portmanteau Theorem.6.The existence and uniqueness of Borel products are proved for Dedekind complete Riesz space-valued σ-measures on completely regular spaces.7.It is shown that weak order convergence of a net of Dedekind complete Riesz space-valued σ-measures is uniform over uniformly bounded, uniformly equicontinuous classes of functions.8.It is shown that every Borel σ-measure on any complete separable metric space is automatically orderly tight in the case that the measure takes values in a weakly σ-distributive, Dedekind complete Riesz space. Less

1.在两个Banach空间值测量值中，显示了Borel注射量张量产物的存在和唯一性以及Fubini-Type定理的有效性。感谢您的结果，拓扑半群上Banach代数值矢量测量值的卷积定义为由其Borel Injective张量产品和半群的操作引起的测量。还证明了Borel注射量张量产物或向量测量的卷积的关节弱连续性。2。证明，对于某些Banach晶格中阳性矢量测量的注入性张量产品对于较弱的载体测量收敛性是共同连续的。 Our approach to this problem is based on Bartle's bilinear vector integration theory.3.Prokhorov-LeCam's compactness criteria and Varadarajan's metrizability criteria are given for vector measurements with values in Frechet spaces, semi-reflexive spaces, and semi-Montel spaces.4.Compactness and sequential compactness criteria are given … More for a set of vector measurements on a complete separate在特定半蒙太德空间中具有值的度量空间。除其他外，还表明，当且仅当相对于相对于通常的弱收敛性相对于通常的弱收敛性相对顺序紧凑时，一组此类矢量测量是统一的，均匀的界限。 From the result one can recognize that not the norm but the order structure on the space where vector measures take values is essential to the validity of the Portmanteau Theorem.6.The existence and uniqueness of Borel products are proven for Dedekind complete Riesz space-valued σ-measures on completely regular spaces.7.It is shown that weak order convergence of a net of Dedekind complete Riesz space-valued σ-measures is uniform over 8.显示，任何完整的单独的度量空间上的每个borelσ量度都会自动订购，以至于测量值在弱σ-分布，Dedekind完整的Riesz空间中，每个单独的度量空间都会自动订购。8。较少的