| Title:
|
Integration by parts formula for McShane and Kurzweil-Henstock integrals via double Lusin condition (English) |
| Author:
|
Racca, Abraham Perral |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0011-4642 |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
151 |
| Issue:
|
2 |
| Year:
|
2026 |
| Pages:
|
221-230 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove an integration by parts formula for McShane and Kurzweil-Henstock integrals utilizing the double Lusin condition. (English) |
| Keyword:
|
McShane integral |
| Keyword:
|
Kurzweil-Henstock integral |
| Keyword:
|
differentiating integral |
| Keyword:
|
integration by parts |
| Keyword:
|
absolute continuity |
| MSC:
|
26A27 |
| MSC:
|
26A39 |
| DOI:
|
10.21136/MB.2025.0150-24 |
| . |
| Date available:
|
2026-05-19T08:21:59Z |
| Last updated:
|
2026-05-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153621 |
| . |
| Reference:
|
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| Reference:
|
[2] Benitez, J. V., Jamil, F. P., Chew, T. S.: Uniform differentiability.Real Anal. Exch. 37 (2011/2012), 451-462. Zbl 1275.26004, MR 3080604, 10.14321/realanalexch.37.2.0451 |
| Reference:
|
[3] Cabral, E., Lee, P.-Y.: A fundamental theorem of calculus for the Kurzweil-Henstock integral in $\Bbb{R}^m$.Real Anal. Exch. 26 (2000/2001), 867-876. Zbl 1024.26005, MR 1844400, 10.2307/44154084 |
| Reference:
|
[4] Chew, T. S.: On Henstock's inner variation and strong derivatives.Real Anal. Exch. 27 (2001/2002), 725-733. Zbl 1069.26008, MR 1923161, 10.14321/realanalexch.27.2.0725 |
| Reference:
|
[5] Chew, T. S., Cabral, E. A., Benitez, J. V.: On the differentiation of Henstock and McShane integrals.Proc. Singapore Nat. Acad. Sci. 15 (2021), 3-8. 10.1142/S2591722621400019 |
| Reference:
|
[6] Gordon, R. A.: The Integrals of Lebegue, Denjoy, Perron, and Henstock.Graduate Studies in Mathematics 4. AMS, Providence (1994). Zbl 0807.26004, MR 1288751, 10.1090/gsm/004 |
| Reference:
|
[7] Henstock, R.: The General Theory of Integration.Oxford Mathematical Monographs. Oxford University Press, Oxford (1991). Zbl 0745.26006, MR 1134656 |
| Reference:
|
[8] Lee, P.-Y.: Lanzhou Lectures on Henstock Integration.Series in Real Analysis 2. World Scientific, Singapore (1989). Zbl 0699.26004, MR 1050957, 10.1142/0845 |
| Reference:
|
[9] Lee, P. Y.: The integral à la Henstock.Sci. Math. Jpn. 67 (2008), 13-21. Zbl 1162.26004, MR 2384584 |
| Reference:
|
[10] Lee, P. Y., Výborný, R.: The Integral: An Easy Approach After Kurzweil and Henstock.Australian Mathematical Society Lecture Series 14. Cambridge University Press, Cambridge (2000). Zbl 0941.26003, MR 1756319 |
| Reference:
|
[11] Lu, J., Lee, P.-Y.: The primitives of Henstock integrable functions in Euclidean space.Bull. Lond. Math. Soc. 31 (1999), 173-180. Zbl 0921.26006, MR 1664188, 10.1112/S0024609398005347 |
| Reference:
|
[12] Racca, A., Cabral, E.: On the double Lusin condition and convergence theorem for Kurzweil-Henstock type integrals.Math. Bohem. 141 (2016), 153-168. Zbl 1389.26015, MR 3499782, 10.21136/MB.2016.13 |
| . |
