A fundamental theorem of calculus for the $M_{\alpha}$-integral
Commun. Korean Math. Soc. 2022 Vol. 37, No. 2, 415-421 https://doi.org/10.4134/CKMS.c210043 Published online March 29, 2022 Printed April 30, 2022
Abraham Perral Racca Adventist University of the Philippines
Abstract : This paper presents a fundamental theorem of calculus, an integration by parts formula and a version of equiintegrability convergence theorem for the $M_{\alpha}$-integral using the $M_{\alpha}$-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 $M_{\alpha}$-strong Lusin condition was imposed.
Keywords : $M_{\alpha}$-integral, $M_{\alpha}$-$SL$, fundamental theorem of calculus, integration by parts
