Sufficient conditions from countably Lipschitz to be strongly generalized absolutely continuous

Christiana Rini Indrati

doi:10.62918/hjma.v1i2.10

Sufficient conditions from countably Lipschitz to be strongly generalized absolutely continuous

Authors

Christiana Rini Indrati Universitas Gadjah Mada

DOI:

https://doi.org/10.62918/hjma.v1i2.10

Keywords:

CL-integral, Countably Lipschitz condition, Henstock-Kurzweil integral, Denjoy integral

Abstract

The CL-integral is an integral that is defined by using countably Lipschitz condition. The CL-integral is more general than the Lebesgue integral, but it is more specific than Denjoy integral in the wide sense. The Denjoy integral in the wide sense is more general than the Henstock-Kurzweil integral. In this paper, it will be given some conditions such that a CL-integrable function is Henctock-Kurzweil-integrable on [a, b].

References

A. M. Bruckner, Fleissner, and J. Foran, The Minimal Integral which includes Lebesgue integrable functions and Derivatives, Colloquium Mathematicum (1986).

Ch.R. Indrati and L. Aryati, 2016, The Countably Lipschitz Integral, Global Journal of Pure and Applied Mathematics 12-5 (2016), pp. 3991-3999.

Ch. R. Indrati and L. Aryati, Initial Value Problems with Countably Lipschitz Condition, Far East Journal of Mathematical Sciences, 103-9, (2018), 1477-1491.

Ch. R. Indrati, 2003, Convergence Theorems for the Henstock Integral Involving Small Riemann Sums, Real Analysis Exchange 29-1, (2003/2004), 481–488.

P. Y. Lee, Lanzhou Lectures on Henstock Integration, World Scientific, Singapore, 1989.

A. W. Schurle, A Function is Perron Integrable if it has locally small Riemann sums, J. Australian Math. Soc (Series A) 41, (1986), 224–232.

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Published

05-05-2023

How to Cite

Indrati, C. R. (2023). Sufficient conditions from countably Lipschitz to be strongly generalized absolutely continuous. Hilbert Journal of Mathematical Analysis, 1(2), 59–64. https://doi.org/10.62918/hjma.v1i2.10