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A generalized Henstock-Stieltjes integral involving division functions

In: Mathematica Slovaca, vol. 58, no. 4
Supriya Pal - D. K. Ganguly - Peng Yee Lee

Details:

Year, pages: 2008, 413 - 438
Keywords:
Henstock integral, $\delta^{k}$-fine division, Saks-Henstock lemma, $GR_k$-integral, \mbox{$GR_k^*$-integral}, weakly $g$-regular function, $SV^{k}[a,b]$, $g$-nearly additive function
About article:
We can consider the Riemann-Stieltjes integral $\intabf \mathrm{d}g$ 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 $\intabf \mathrm{d}g$ 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.
How to cite:
ISO 690:
Pal, S., Ganguly, D., Lee, P. 2008. A generalized Henstock-Stieltjes integral involving division functions. In Mathematica Slovaca, vol. 58, no.4, pp. 413-438. 0139-9918.

APA:
Pal, S., Ganguly, D., Lee, P. (2008). A generalized Henstock-Stieltjes integral involving division functions. Mathematica Slovaca, 58(4), 413-438. 0139-9918.