La substitution dans les intégrales de Riemann-Stieltjes
Lebesgue's Convergence Theorem of Complex-Valued Function
In this article, we formalized Lebesgue's Convergence theorem of complex-valued function. We proved Lebesgue's Convergence Theorem of realvalued function using the theorem of extensional real-valued function. Then applying the former theorem to real part and imaginary part of complex-valued functional sequences, we proved Lebesgue's Convergence Theorem of complex-valued function. We also defined partial sums of real-valued functional sequences and complex-valued functional sequences and showed their...
Lebesgueův integrál v abstraktních prostorech
Linear integral equations in the space of regulated functions.
Linear operators in the space of regulated functions
Representation of bounded and compact linear operators in the Banach space of regulated functions is given in terms of Perron-Stieltjes integral.
Linear Stieltjes integral equations in Banach spaces
Fundamental results concerning Stieltjes integrals for functions with values in Banach spaces have been presented in [5]. The background of the theory is the Kurzweil approach to integration, based on Riemann type integral sums (see e.g. [3]). It is known that the Kurzweil theory leads to the (non-absolutely convergent) Perron-Stieltjes integral in the finite dimensional case. Here basic results concerning equations of the form x(t) = x(a) +at [A(s)]x(s) +f(t) - f(a) are presented on the basis of...
Lokale Integralnomen und verallgemeinerte uneigentliche Riemann-Stieltjes-Integrale.