A NONLINEAR HENSTOCK-TYPE INTEGRAL FOR RIESZ SPACE-VALUED FUNCTIONS

被引：0

作者：

Fatkhurrohman, Muhammad ^{[1
]}

Tantrawan, Made ^{[1
]}

机构：

[1] Univ Gadjah Mada, Fac Math & Nat Sci, Dept Math, Yogyakarta 55281, Indonesia

来源：

BULLETIN OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2025年 / 17卷 / 02期

关键词：

nonlinear integral; Henstock integral; Riesz space;

D O I：

10.54671/BMAA-2025-2-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we introduce a nonlinear extension of the Henstock integral for functions taking values in a Riesz space. By combining the conditions provided in Lee (1989) for the real case with Fremlins (D)-double sequence technique, we establish several fundamental properties of the integral, including a Cauchy-type criterion and the integrability of step functions and (D)-continuous functions. Furthermore, we demonstrate that the SaksHenstock lemma holds for this integral and prove the absolute (D)-continuity of its primitive.

引用

页码：26 / 39

页数：14

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[10]

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