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.
On the product of derivatives
On the relationships between Stieltjes type integrals of Young, Dushnik and Kurzweil
In this paper we explain the relationship between Stieltjes type integrals of Young, Dushnik and Kurzweil for functions with values in Banach spaces. To this aim also several new convergence theorems will be stated and proved.
On the strong McShane integral of functions with values in a Banach space
The classical Bochner integral is compared with the McShane concept of integration based on Riemann type integral sums. It turns out that the Bochner integrable functions form a proper subclass of the set of functions which are McShane integrable provided the Banach space to which the values of functions belong is infinite-dimensional. The Bochner integrable functions are characterized by using gauge techniques. The situation is different in the case of finite-dimensional valued vector functions....
On the Volterra integral equation and the Henstock-Kurzweil integral.
On the Ward Theorem for -adic-path bases associated with a bounded sequence
In this paper we prove that each differentiation basis associated with a -adic path system defined by a bounded sequence satisfies the Ward Theorem.
On the -finiteness of a variational measure
The -finiteness of a variational measure, generated by a real valued function, is proved whenever it is -finite on all Borel sets that are negligible with respect to a -finite variational measure generated by a continuous function.
On totalization of the Kurzweil-Henstock integral in the multidimensional space
In this paper a full totalization is presented of the Kurzweil-Henstock integral in the multidimensional space. A residual function of the total Kurzweil-Henstock primitive is defined.
On variations of functions of one real variable
We discuss variations of functions that provide conceptually similar descriptive definitions of the Lebesgue and Denjoy-Perron integrals.
On ω-approximately continuous Denjoy-Steiltjes integral
Operator-valued functions of bounded semivariation and convolutions
The abstract Perron-Stieltjes integral in the Kurzweil-Henstock sense given via integral sums is used for defining convolutions of Banach space valued functions. Basic facts concerning integration are preseted, the properties of Stieltjes convolutions are studied and applied to obtain resolvents for renewal type Stieltjes convolution equations.
Ordinary differential equations the solution of which are -functions