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A FUNDAMENTAL THEOREM OF CALCULUS FOR THE M<sub>α</sub>-INTEGRAL
A FUNDAMENTAL THEOREM OF CALCULUS FOR THE M<sub>α</sub>-INTEGRAL
- 대한수학회
- Communications of the Korean Mathematical Society
- Vol.37 No.2
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2022.01415 - 421 (7 pages)
- 0
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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.
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