Maple tools for the Kurzweil integral
Riemann sums based on -fine partitions are illustrated with a Maple procedure.
McShane equi-integrability and Vitali’s convergence theorem
The McShane integral of functions defined on an -dimensional interval is considered in the paper. This integral is known to be equivalent to the Lebesgue integral for which the Vitali convergence theorem holds. For McShane integrable sequences of functions a convergence theorem based on the concept of equi-integrability is proved and it is shown that this theorem is equivalent to the Vitali convergence theorem.
Multipliers for generalized Riemann integrals in the real line
We use an elementary method to prove that each function is a multiplier for the -integral.