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On the Relation between Denjoy–Khintchine and $ \operatorname{HK}_{r} $ -Integrals
Siberian Mathematical Journal ( IF 0.5 ) Pub Date : 2024-03-01 , DOI: 10.1134/s0037446624020162 V. A. Skvortsov , P. Sworowski
中文翻译:
关于 Denjoy–Khintchine 与 $ \operatorname{HK}_{r} $ -Integrals 之间的关系
更新日期:2024-03-01
Siberian Mathematical Journal ( IF 0.5 ) Pub Date : 2024-03-01 , DOI: 10.1134/s0037446624020162 V. A. Skvortsov , P. Sworowski
Abstract
We locate Musial and Sagher’s concept of \( \operatorname{HK}_{r} \) -integration within the approximate Henstock–Kurzweil integral theory. If we restrict the \( \operatorname{HK}_{r} \) -integral by the requirement that the indefinite \( \operatorname{HK}_{r} \) -integral is continuous, then it becomes included in the classical Denjoy–Khintchine integral. We provide a direct argument demonstrating that this inclusion is proper.
中文翻译:
关于 Denjoy–Khintchine 与 $ \operatorname{HK}_{r} $ -Integrals 之间的关系
摘要
我们将 Musial 和 Sagher 的\( \operatorname{HK}_{r} \)积分概念定位在近似的 Henstock-Kurzweil 积分理论中。如果我们通过不定的\(\operatorname{HK}_{r} \) -积分是连续的要求来限制\( \operatorname{HK}_{r} \) -积分,那么它就包含在经典中Denjoy-Khinchine 积分。我们提供了一个直接的论据来证明这种包含是正确的。