Abstract
We confine our attention to convergence theorems and descriptive relationships within some subclasses of Riemann-measurable vector-valued functions that are based on the various generalizations of the Riemann definition of an integral.
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Research of K. Naralenkov was partially supported by F.F.R. of the University of Palermo. The third named author expresses his appreciation to the University of Palermo Department of Mathematics and Computer Science for its hospitality in summer 2015, during which part of this research was carried out.
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Caponetti, D., Marraffa, V. & Naralenkov, K. On the integration of Riemann-measurable vector-valued functions. Monatsh Math 182, 513–536 (2017). https://doi.org/10.1007/s00605-016-0923-z
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DOI: https://doi.org/10.1007/s00605-016-0923-z
Keywords
- Birkhoff, McShane, Henstock, and Pettis integrals
- Lebesgue measurable gauge
- Riemann-measurable function
- Almost uniform convergence
- Bounded variation
- \(ACG_{*}\) and \(ACG_{\delta }^{*}\) functions