RIEMANN AND RIEMANN-TYPE INTEGRATION IN BANACH SPACES

Sk. Jaker Ali; Pratikshan Mondal

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RIEMANN AND RIEMANN-TYPE INTEGRATION IN BANACH SPACES

机译：Banach空间中的RIEMANN和RIEMANN型积分

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Riemann, Riemann-Dunford, Riemann-Pettis and Darboux integrable functions with values in a Banach space and Riemann-Gelfand integrable functions with values in the dual of a Banach space are studied in the light of the work of Graves, Alexiewicz and Orlicz, and Gordon. Various properties of these types of integrals and the interrelation between them are established. The Fundamental Theorem of Integral Calculus for these types of integrals is also studied.

机译：根据Graves，Alexiewicz和Orlicz的工作，研究了Banach空间中带值的Riemann，Riemann-Dunford，Riemann-Pettis和Darboux可积函数，以及Banach空间对偶的Riemann-Gelfand可积函数。戈登。建立了这些类型的积分的各种性质以及它们之间的相互关系。对于这些类型的积分，还研究了积分微积分的基本定理。

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来源
《Real analysis exchange》 |2014年第2期|403-440|共38页
作者
Sk. Jaker Ali; Pratikshan Mondal;
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作者单位

Department of Mathematics, Bolpur College, Bolpur, Birbhum - 731204, West Bengal, India;

Department of Mathematics, Durgapur Government College, Durgapur - 713214, Burdwan, West Bengal, India;

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原文格式 PDF
正文语种 eng
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关键词
Riemann integral; Darboux integral; Riemann-Dunford integral; Riemann-Pettis integral; Riemann-Gelfand integral; Bochner integrable equivalent;

机译：黎曼积分Darboux积分;黎曼-邓福德积分;黎曼-佩蒂斯积分;Riemann-Gelfand积分;Bochner可积等价物;

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专利

1. EQUI-RIEMANN AND EQUI-RIEMANN-TYPE INTEGRABLE FUNCTIONS WITH VALUES IN A BANACH SPACE [J] . Pratikshan Mondal, Lakshmi Kanta Dey, Sk. Jaker Ali Real analysis exchange . 2018,第2期

机译：Banach空间中带值的等值齐整型和等值齐整型
2. ASYMPTOTIC STRUCTURE OF BANACH SPACES AND RIEMANN INTEGRATION [J] . K. M. Naralenkov Real analysis exchange . 2008,第1期

机译：Banach空间的渐近结构与Rimann积分。
3. A RIEMANN-TYPE INTEGRAL ON A MEASURE SPACE [J] . Giuseppa Riccobono Real analysis exchange . 2005,第1期

机译：测量空间上的RIEMANN型积分
4. Conditions for stochastic integrability in UMD Banach spaces [C] . Jan van Neerven, Mark Veraar, Lutz Weis Banach Spaces and Their Applications in Analysis . 2007

机译：UMD Banach空间中随机积分的条件
5. Invariant subspace problem and spectral properties of bounded linear operators on Banach spaces, Banach lattices, and topological vector spaces [D] . Troitsky, Vladimir G. 1999

机译：Banach空间，Banach格和拓扑矢量空间上有界线性算子的不变子空间问题和谱性质
6. A new inequality for the Riemann-Stieltjes integrals driven by irregular signals in Banach spaces [O] . Rafał M Łochowski -1

机译：Banach空间中不规则信号驱动的Riemann-Stieltjes积分的新不等式
7. Quasi-uniform and uniform convergence of Riemann and Riemann-type integrable functions with values in a Banach space [O] . Pratikshan Mondal, Lakshmi Dey, Ali Jaker 2020

机译：riemann和riemann型可积函数的准均匀和均匀融合，具有Banach空间中的值
8. Lyapounov Convexity Theorem and Riemann-Type Integrals, [R] . artstein, zvi 1975

机译：Lyapounov凸性定理和Riemann型积分，

RIEMANN AND RIEMANN-TYPE INTEGRATION IN BANACH SPACES

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