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1995/1996 On generalized convergence theorems for Thomson’s ℬ-integral on ℝm
Ying-Jian Lin
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Real Anal. Exchange 21(1): 365-379 (1995/1996).


In this paper, we extend the \({\mathcal{B}}\)-integral on \(\mathbb{R}\) to one on \(\mathbb{R}^{m}\). After proving a weaker version of the equiintegrability theorem, the equivalence of five generalized convergence theorems will be established, which include the equiintegrability theorem, two versions of the generalized controlled convergence theorem which are based on \(UACG^\nabla\) and \(UACG_{\mathcal{B}}^{\ast\ast}\), respectively, the generalized variational convergence theorem and the uniformly \(MGSRS_{\mathcal{B}}\) (modified \(GSRS\) with respect to \({\mathcal{B}}\)) convergence theorem.


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Ying-Jian Lin. "On generalized convergence theorems for Thomson’s ℬ-integral on ℝm." Real Anal. Exchange 21 (1) 365 - 379, 1995/1996.


Published: 1995/1996
First available in Project Euclid: 3 July 2012

MathSciNet: MR1377551

Primary: 26A39

Keywords: Thomson's B-integral

Rights: Copyright © 1995 Michigan State University Press

Vol.21 • No. 1 • 1995/1996
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