On Fubini theorem for general Perron integral
On Henstock-Dunford and Henstock-Pettis integrals.
On Henstock-Kurzweil method to Stratonovich integral
We use the general Riemann approach to define the Stratonovich integral with respect to Brownian motion. Our new definition of Stratonovich integral encompass the classical Stratonovich integral and more importantly, satisfies the ideal Itô formula without the “tail” term, that is, Further, the condition on the integrands in this paper is weaker than the classical one.
On indefinite BV-integrals
We present an example of a locally BV-integrable function in the real line whose indefinite integral is not the sum of a locally absolutely continuous function and a function that is Lipschitz at all but countably many points.
On Itô-Kurzweil-Henstock integral and integration-by-part formula
In this paper we derive the Integration-by-Parts Formula using the generalized Riemann approach to stochastic integrals, which is called the Itô-Kurzweil-Henstock integral.
On Kurzweil-Henstock equiintegrable sequences
For the Kurzweil-Henstock integral the equiintegrability of a pointwise convergent sequence of integrable functions implies the integrability of the limit function and the relation m abfm(s)s = abm fm(s)s. Conditions for the equiintegrability of a sequence of functions pointwise convergent to an integrable function are presented. These conditions are given in terms of convergence of some sequences of integrals.
On Kurzweil-Stieltjes equiintegrability and generalized BV functions
We present sufficient conditions ensuring Kurzweil-Stieltjes equiintegrability in the case when integrators belong to the class of functions of generalized bounded variation.
On Kurzweil-Stieltjes integral in a Banach space
In the paper we deal with the Kurzweil-Stieltjes integration of functions having values in a Banach space We extend results obtained by Štefan Schwabik and complete the theory so that it will be well applicable to prove results on the continuous dependence of solutions to generalized linear differential equations in a Banach space. By Schwabik, the integral exists if has a bounded semi-variation on and is regulated on We prove that this integral has sense also if is regulated on ...
On Lebesgue measurability of Henstock-Kurzweil integrable functions.
On Mawhin's approach to multiple nonabsolutely convergent integral
On McShane-type integrals with respect to some derivation bases
Some observations concerning McShane type integrals are collected. In particular, a simple construction of continuous major/minor functions for a McShane integrand in is given.
On multiplication of Perron-integrable functions
On non-absolutely convergent integrals
The influence of Jan Marik in the field of non absolute integration is described in the plane of Czech mathematics. A short historical account on the development of integration theory in the Czech region is presented in this connection together with the recent Riemann sum approach to the general Perron integral.
On representations of some Perron integrable functions
On Riemann-type definition for the wide Denjoy integral
On the approximate Peano derivatives
On the derivative of indefinite RC-integral
On the double Lusin condition and convergence theorem for Kurzweil-Henstock type integrals
Equiintegrability in a compact interval may be defined as a uniform integrability property that involves both the integrand and the corresponding primitive . The pointwise convergence of the integrands to some and the equiintegrability of the functions together imply that is also integrable with primitive and that the primitives converge uniformly to . In this paper, another uniform integrability property called uniform double Lusin condition introduced in the papers E. Cabral...
On the failure of a decomposition
On the Kurzweil integral for functions with values in ordered spaces. II.