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A generalized Henstock-Stieltjes integral involving division functions |
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| Authors: | Supriya Pal D K Ganguly Lee Peng Yee |
| Institution: | (1) Serampore College, Serampore, Hooghly West-Bengal, PIN-712201, India;(2) Department of Pure Mathematics, University of Calcutta, 35, Ballygunge Circular road, Calcutta, 700019, India;(3) MME, National Institute of Education, 1 Nanyang Walk, Singapore, 637616, Singapore |
| Abstract: | We can consider the Riemann-Stieltjes integral  dg as an integral of a point function f with respect to an interval function g. We could extend it to the Henstock-Stieltjes integral. In this paper, we extend it to a generalized Stieltjes integral  dg of a point function f with respect to a function g of divisions of an interval. Then we prove for this integral the standard results in the theory of integration, including
the controlled convergence theorem.
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| Keywords: | Henstock integral δ k -fine division Saks-Henstock lemma GR k -integral GR k *-integral weakly g-regular function SV k [a b] g-nearly additive function |
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