Regulated functions and the Perron-Stieltjes integral
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Remarques sur l'intégrale de Riemann généralisée
Shrishti Dhav Chatterji (1996)
Séminaire de probabilités de Strasbourg
Riemann-type definition of the improper integrals
Donatella Bongiorno (2004)
Czechoslovak Mathematical Journal
Riemann-type definitions of the Riemann improper integral and of the Lebesgue improper integral are obtained from McShane’s definition of the Lebesgue integral by imposing a Kurzweil-Henstock’s condition on McShane’s partitions.
Role of the Harnack extension principle in the Kurzweil-Stieltjes integral
Umi Mahnuna Hanung (2024)
Mathematica Bohemica
In the theories of integration and of ordinary differential and integral equations, convergence theorems provide one of the most widely used tools. Since the values of the Kurzweil-Stieltjes integrals over various kinds of bounded intervals having the same infimum and supremum need not coincide, the Harnack extension principle in the Kurzweil-Henstock integral, which is a key step to supply convergence theorems, cannot be easily extended to the Kurzweil-type Stieltjes integrals with discontinuous...
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