Elementary construction of Hölder functions such that the Kurzweil-Stieltjes integral does not exist
For any with we provide a simple construction of an -Hölde function and a -Hölder function such that the integral fails to exist even in the Kurzweil-Stieltjes sense.
Erster Cursus der Differential- und Integralrechnung nebst einer Sammlung von 1450 Beispielen und Übungsaufgaben zum Gebrauche an höheren Lehranstalten und beim Selbststudium [Book]
Étude sur les formules d'approximation qui servent à calculer la valeur numérique d'une intégrale définie.
Every -integrable function is Pfeffer integrable
Extrait d'une Lettre adressée à M. Besge.
Extrait d'une lettre adressée à M. Hermite
Extrait d'une Lettre adressée à M. Liouville.
Fields of sets, set functions, set function integrals, and finite additivity.
Formules relatives à, la théprie des intégrales définies
Functions Riemann-Stieltjes integrable against themselves
General integration and extensions. I
A general concept of integral is presented in the form given by S. Saks in his famous book Theory of the Integral. A special subclass of integrals is introduced in such a way that the classical integrals (Newton, Riemann, Lebesgue, Perron, Kurzweil-Henstock...) belong to it. A general approach to extensions is presented. The Cauchy and Harnack extensions are introduced for general integrals. The general results give, as a specimen, the Kurzweil-Henstock integration in the form of the extension of...
General integration and extensions.II
This work is a continuation of the paper (Š. Schwabik: General integration and extensions I, Czechoslovak Math. J. 60 (2010), 961–981). Two new general extensions are introduced and studied in the class of general integrals. The new extensions lead to approximate description of the Kurzweil-Henstock integral based on the Lebesgue integral close to the results of S. Nakanishi presented in the paper (S. Nakanishi: A new definition of the Denjoy’s special integral by the method of successive approximation,...
Generalized multiple Perron integrals and the Green-Goursat theorem for differentiable vector fields
Generalized ordinary differential equations and discrete systems
Grundlagen für eine Theorie der Functionen einer veränderlichen rellen Grösse [Book]
Integral de Riemann num espaço topológico geral
Integral of Complex-Valued Measurable Function
In this article, we formalized the notion of the integral of a complex-valued function considered as a sum of its real and imaginary parts. Then we defined the measurability and integrability in this context, and proved the linearity and several other basic properties of complex-valued measurable functions. The set of properties showed in this paper is based on [15], where the case of real-valued measurable functions is considered.MML identifier: MESFUN6C, version: 7.9.01 4.101.1015
Integral of multivalued mappings and its connection with differential relations
Integral of Real-Valued Measurable Function 1
Based on [16], authors formalized the integral of an extended real valued measurable function in [12] before. However, the integral argued in [12] cannot be applied to real-valued functions unconditionally. Therefore, in this article we have formalized the integral of a real-value function.