ON UNIFORMLY DISTRIBUTED SEQUENCES OF AN INCREASING FAMILY OF FINITE SETS IN INFINITE-DIMENSIONAL RECTANGLES

Gogi   Pantsulaia

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ON UNIFORMLY DISTRIBUTED SEQUENCES OF AN INCREASING FAMILY OF FINITE SETS IN INFINITE-DIMENSIONAL RECTANGLES

机译：无限维矩形中有限集族的一致分布序列

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摘要

The concepts of uniformly distributed sequences of an increasing family of finite sets and Riemann integrability are considered in terms of the "Lebesgue measure" on infinite-dimensional rectangles in R~∞ and infinite-dimensional versions of famous results of Lebesgue and Weyl are proved.

机译：根据R〜∞中无限维矩形上的“ Lebesgue测度”，考虑了有限集族的均匀分布序列和Riemann可积性的概念，并证明了Lebesgue和Weyl的著名结果的无限维形式。

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来源
《Real analysis exchange》 |2011年第2期|p.325-340|共16页
作者
Gogi Pantsulaia;
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作者单位

Department of Mathematics, Georgian Technical University, Tbilisi, 0175, Georgia I.Vekua Institute of Applied Mathematics, Tbilisi State University, Tbilisi 0143, Georgia;

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原文格式 PDF
正文语种 eng
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关键词
infinite-dimensional Lebesgue measure; Riemann integral; uniformly dis-tributed sequences;

机译：无限维Lebesgue测度;黎曼积分;均匀分布序列;

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专利

1. On Uniformly Distributed Dilates of Finite Integer Sequences [J] . S. V. Konyagin, I. Z. Ruzsa, W. Schlag Journal of Number Theory . 2000,第2期

机译：有限整数序列的一致分布扩张
2. A new mapping for finding a common element of the sets of fixed points of two finite families of nonexpansive and strictly pseudo-contractive mappings and two sets of variational inequalities in uniformly convex and 2-smooth Banach spaces [J] . Atid Kangtunyakarn Fixexd point theory and applications . 2013,第1期

机译：在一致凸和2光滑Banach空间中寻找两个有限族的非扩张和严格伪压缩映射的不动点集的公共元素和两组变分不等式的新映射
3. A new mapping for finding a common element of the sets of fixed points of two finite families of nonexpansive and strictly pseudo-contractive mappings and two sets of variational inequalities in uniformly convex and 2-smooth Banach spaces [J] . Atid Kangtunyakarn Fixexd point theory and applications . 2013,第1期

机译：在一致凸和2光滑Banach空间中寻找两个有限族的非扩张和严格伪压缩映射的不动点集的公共元素和两组变分不等式的新映射
4. Extension of family size of ZCZ sequence sets derived from perfect sequences and unitary matrices [C] . Torii, H., Nakamura, . 2002

机译：源自完美序列和unit矩阵的ZCZ序列集的族大小的扩展
5. Markov chain Monte Carlo algorithms using completely uniformly distributed driving sequences [D] . Tribble, Seth D. 2007

机译：马尔可夫链Monte Carlo算法使用完全均匀分布的驱动序列
6. Distributed Space Debris Tracking with Consensus Labeled Random Finite Set Filtering [O] . Baishen Wei, Brett Nener 2018

机译：带有共识标签的随机有限集滤波的分布式空间碎片跟踪
7. On Uniformly Distributed Dilates of Finite Integer Sequences [O] . Konyagin S.V, Ruzsa I.Z, Schlag W 2000

机译：有限整数序列的一致分布扩张
8. Infinite-Dimensional Generalization of Shilov Boundary and Infinite-Dimensional Analytic Structures in the Spectrum of a Uniform Algebra [R] . Tonev, T. V. 1986

机译：均匀代数谱中shilov边界和无限维分析结构的无限维推广

ON UNIFORMLY DISTRIBUTED SEQUENCES OF AN INCREASING FAMILY OF FINITE SETS IN INFINITE-DIMENSIONAL RECTANGLES

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