The Hilbert-type integral inequalities with a homogeneous kernel of -degree.
The Hlawka-Djoković inequality and points in unitary spaces.
The Hurewicz covering property and slaloms in the Baire space
According to a result of Kočinac and Scheepers, the Hurewicz covering property is equivalent to a somewhat simpler selection property: For each sequence of large open covers of the space one can choose finitely many elements from each cover to obtain a groupable cover of the space. We simplify the characterization further by omitting the need to consider sequences of covers: A set of reals X has the Hurewicz property if, and only if, each large open cover of X contains a groupable subcover. This...
The inequalities in variables.
The inequality of Milne and its converse. II.
The inner periodic structure of a function.
The insertion of sets and fine topologies
The intersection convolution of relations and the Hahn-Banach type theorems
By introducing the intersection convolution of relations, we prove a natural generalization of an extension theorem of B. Rodrí guez-Salinas and L. Bou on linear selections which is already a substantial generalization of the classical Hahn-Banach theorems. In particular, we give a simple neccesary and sufficient condition in terms of the intersection convolution of a homogeneous relation and its partial linear selections in order that every partial linear selection of this relation can have an...
The iterates are not dense in .
The Kurzweil construction of an integral in ordered spaces
This paper generalizes the results of papers which deal with the Kurzweil-Henstock construction of an integral in ordered spaces. The definition is given and some limit theorems for the integral of ordered group valued functions defined on a Hausdorff compact topological space with respect to an ordered group valued measure are proved in this paper.
The Kurzweil integral in financial market modeling
Certain financial market strategies are known to exhibit a hysteretic structure similar to the memory observed in plasticity, ferromagnetism, or magnetostriction. The main difference is that in financial markets, the spontaneous occurrence of discontinuities in the time evolution has to be taken into account. We show that one particular market model considered here admits a representation in terms of Prandtl-Ishlinskii hysteresis operators, which are extended in order to include possible discontinuities...
The Kurzweil integral with exclusion of negligible sets
We propose an extended version of the Kurzweil integral which contains both the Young and the Kurzweil integral as special cases. The construction is based on a reduction of the class of -fine partitions by excluding small sets.
The Kurzweil-Henstock theory of stochastic integration
The Kurzweil-Henstock approach has been successful in giving an alternative definition to the classical Itô integral, and a simpler and more direct proof of the Itô Formula. The main advantage of this approach lies in its explicitness in defining the integral, thereby reducing the technicalities of the classical stochastic calculus. In this note, we give a unified theory of stochastic integration using the Kurzweil-Henstock approach, using the more general martingale as the integrator. We derive...
The Henstock-Kurzweil integral
We present a method of integration along the lines of the Henstock-Kurzweil integral. All -derivatives are integrable in this method.
The laminary model of the exploded Descartes-plane.
The Laplace derivative
A function is said to have the -th Laplace derivative on the right at if is continuous in a right neighborhood of and there exist real numbers such that converges as for some . There is a corresponding definition on the left. The function is said to have the -th Laplace derivative at when these two are equal, the common value is denoted by . In this work we establish the basic properties of this new derivative and show that, by an example, it is more general than the generalized...
The Lebesgue integral a little over 100 years later.
The Lebesgue integral as a Riemann integral.
The length of a lemmiscate.
The level function in rearrangement invariant spaces.
An exact expression for the down norm is given in terms of the level function on all rearrangement invariant spaces and a useful approximate expression is given for the down norm on all rearrangement invariant spaces whose upper Boyd index is not one.