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A FUNDAMENTAL THEOREM OF CALCULUS FOR THE M<sub>α</sub>-INTEGRAL
Racca, Abraham Perral Korean Mathematical Society 2022 대한수학회논문집 Vol.37 No.2
This paper presents a fundamental theorem of calculus, an integration by parts formula and a version of equiintegrability convergence theorem for the M<sub>α</sub>-integral using the M<sub>α</sub>-strong Lusin condition. In the convergence theorem, to be able to relax the condition of being point-wise convergent everywhere to point-wise convergent almost everywhere, the uniform M<sub>α</sub>-strong Lusin condition was imposed.
Characterizing Convergence Conditions for the M_α-Integral
Ian June Luzon Garces,Abraham Perral Racca 충청수학회 2011 충청수학회지 Vol.24 No.3
Park, Ryu, and Lee recently defined a Henstock-type integral, which lies entirely between the McShane and the Henstock integrals. This paper presents two characterizing convergence conditions for this integral, and derives other known convergence theorems as corollaries.
CHARACTERIZING CONVERGENCE CONDITIONS FOR THE Ma-INTEGRAL
Ian June Luzon Garces,Abraham Perral Racca 충청수학회 2011 충청수학회지 Vol.25 No.3
Park, Ryu, and Lee recently de¯ned a Henstock-type integral, which lies entirely between the McShane and the Hen- stock integrals. This paper presents two characterizing convergence conditions for this integral, and derives other known convergence theorems as corollaries.