Communications of the
Korean Mathematical Society CKMS

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

MSC numbers: Primary 26A39