A generalized Henstock-Stieltjes integral involving division functions

Mathematica Slovaca

Supriya Pal¹  Lee Yee¹  D. Ganguly¹ 

关键词: Henstock integral;    δk-fine division;    Saks-Henstock lemma;    GRk-integral;    GRk*-integral;    weakly g-regular function;    SVk[a;    b];    g-nearly additive function;   

DOI  :  10.2478/s12175-008-0085-0

学科分类：数学（综合）

来源: Slovenska Akademia Vied * Matematicky Ustav / Slovak Academy of Sciences, Mathematical Institute

【 摘 要 】

We can consider the Riemann-Stieltjes integral $$intlimits_a^b f $$ dg 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 $$intlimits_a^b f $$ dg 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.

【 授权许可】

Unknown