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Matematicheskaya Fizika, Analiz, Geometriya [Mathematical Physics, Analysis, Geometry], 2000, Volume 7, Number 1, Pages 49–65
(Mi jmag393)
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This article is cited in 15 scientific papers (total in 15 papers)
On “integration” of non-integrable vector-valued functions
V. M. Kadets, L. M. Tseytlin Department of Mathematics and Mechanics, Kharkov National University, 4 Svobody Sq., Kharkov, 61077, Ukraine
Abstract:
A new definition of the integral for functions with values in Banach spaces is presented. The new integrability is a weaker property than the Bochner integrability but stronger than the Pettis one. This new definition leads naturally to the notion of the limit set of integral sums, which may be considered as a “generalized integral” for non-integrable functions. This set is shown to be always convex and non-empty when the function has an integrable majorant and the space is separable or reflexive.
Received: 23.02.1998
Citation:
V. M. Kadets, L. M. Tseytlin, “On “integration” of non-integrable vector-valued functions”, Mat. Fiz. Anal. Geom., 7:1 (2000), 49–65
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https://www.mathnet.ru/eng/jmag393 https://www.mathnet.ru/eng/jmag/v7/i1/p49
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Abstract page: | 279 | Full-text PDF : | 166 |
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