共查询到20条相似文献,搜索用时 62 毫秒
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给出集值Bartle积分一个新的定义,并进一步讨论了数值函数关于有界闭凸集值可数可加集值测度的积分的性质,建立了集值Bartle积分的新的极限定理. 相似文献
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林一星 《纯粹数学与应用数学》2010,26(5):872-880
由有界变差向量值测度的值域,通过取凸包和闭包,构造了L[0,1],L2[0,1]和C[0,1]空间上的有界变差紧凸集值测度,结果由欧氏空间推广到函数空间. 相似文献
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集值Lebesgue—Stieltjes积分 总被引:8,自引:2,他引:6
本文首先刻划了B(R_ )上的集值测度,其次建立了(R_ B(R_ ))上的集值Lebesgue-Stieltjes积分.最后,进—步建立了集值随机Lebesgue-Stietjes积分的理论. 相似文献
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F.Hiai在集值测度有界变差的条件下,给出了Aumann积分的R-N性质,本文在集值测度为σ-有界变差的条件下,建立了集值测度表示成Pettis-Aumann积分的充要条件。 相似文献
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本文建立了 Banach空间集值测度的 Radon-Nikodym定理,并给出了两类集值算子的Pettis-Aumann积分表示. 相似文献
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本文建立了Banach空间集值测度的Radon-Nikodym定理,并给出了两类集值算子的Pettis-Aumann积分表示. 相似文献
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本文建立了 Banach空间集值测度的 Radon-Nikodym定理,并给出了两类集值算子的Pettis-Aumann积分表示. 相似文献
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Nikolaos S Papageorgiou 《Journal of multivariate analysis》1985,17(2):207-227
This second part of the work on Banach space valued multifunctions begins with a detailed study of set valued martingales, which have their values in a Banach space. Several new convergence theorems are established for different modes of convergence. The profile of a multifunction in connection with set valued martingales is also studied. The notion of weak convergence of multifunctions is introduced and used to obtain additional convergence theorems for set valued martingales. In the last two sections of the paper set valued measures dealt with and an integral with respect to a set valued measure is introduced. 相似文献
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吴健荣 《纯粹数学与应用数学》2001,17(4):370-376
对集值映射的Pettis-Aumann型积分的性质作了讨论,给出了Pettis-Aumann积分型积分的Fatou引理形式以及其它一些收敛定理,探讨了带参数集值映射的积分性质。 相似文献
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On the hellinger square integral with respect to an operator valued measure and stationary processes
Andrzej Makagon 《Journal of multivariate analysis》1984,14(1):114-133
A construction of the Hellinger square integral with respect to a semispectral measure in a Banach space B is given. It is proved that the space of values of a B-valued stationary stochastic process is unitarily isomorphic to the space of all B1-valued measures that are Hellinger square integrable with respect to the spectral measure of the process. Some applications of the above theorem in the prediction theory (especially to interpolation problem) are also considered. 相似文献
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In this paper,we consider numerical and trigonometric series with a very general monotonicity condition.First,a fundamental decomposition is established from which the sufficient parts of many classical results in Fourier analysis can be derived in this general setting.In the second part of the paper a necessary and sufficient condition for the uniform convergence of sine series is proved generalizing a classical theorem of Chaundy and Jolliffe. 相似文献
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Nikolaos S Papageorgiou 《Proceedings Mathematical Sciences》1991,101(2):63-70
In this paper we prove some convergence theorems for Banach space valued multifunctions. First we consider the notion of weak
convergence of sets and prove a weak completeness and a weak compactness result of the Dunford-Pettis type for weakly compact,
convex valued integrable multifunctions. Then we consider set valued martingales and establish two convergence theorems. One
using the Kuratowski-Mosco mode of convergence and for the other the Hausdorff mode. 相似文献
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A.U. Kussmaul 《Journal of multivariate analysis》1980,10(1):107-122
A new technique is developed which allows to study quasimartingales with values in a Banach space E via real quasimartingales. As a byproduct path compactness for a wide class of E-valued quasimartingales is proved. The first application of this technique yields the equivalence of a.s. convergence and path compactness for E-valued martingales. Furthermore local decomposability of an E-valued semimartingale into a square integrable martingale and a process of integrable variation is established. Finally, it is shown that each process of integrable variation, with values in a Banach space with Radon-Nikodym property, can be approximated by processes taking values in a finite-dimensional subspace. 相似文献
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