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 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 weighted Hadamard-type singular integrals and their applications.
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.
Orthogonally additive functionals on
In this paper we give a representation theorem for the orthogonally additive functionals on the space in terms of a non-linear integral of the Henstock-Kurzweil-Stieltjes type.
Počet integrální [Book]
Pointwise limits for sequences of orbital integrals
In 1967, Ross and Stromberg published a theorem about pointwise limits of orbital integrals for the left action of a locally compact group G on (G,ρ), where ρ is the right Haar measure. We study the same kind of problem, but more generally for left actions of G on any measure space (X,μ), which leave the σ-finite measure μ relatively invariant, in the sense that sμ = Δ(s)μ for every s ∈ G, where Δ is the modular function of G. As a consequence, we also obtain a generalization of a theorem of Civin...
Poznámka k větě o substituci pro Riemannův integrál
Poznámka k větě o substituci pro Riemannův integrál
Question d'examen
Réponse à la Lettre précédente.
Riemann Integral of Functions from ℝ into Real Banach Space
In this article we deal with the Riemann integral of functions from R into a real Banach space. The last theorem establishes the integrability of continuous functions on the closed interval of reals. To prove the integrability we defined uniform continuity for functions from R into a real normed space, and proved related theorems. We also stated some properties of finite sequences of elements of a real normed space and finite sequences of real numbers. In addition we proved some theorems about the...
Riemann Integral of Functions from R into n -dimensional Real Normed Space
In this article, we define the Riemann integral on functions R into n-dimensional real normed space and prove the linearity of this operator. As a result, the Riemann integration can be applied to the wider range. Our method refers to the [21].
Riemann Integral of Functions from R into R n
In this article, we define the Riemann Integral of functions from R into Rn, and prove the linearity of this operator. The presented method is based on [21].
Riemann Integral of Functions from R into Real Normed Space
In this article, we define the Riemann integral on functions from R into real normed space and prove the linearity of this operator. As a result, the Riemann integration can be applied to a wider range of functions. The proof method follows the [16].
Riemann Integral of Functions R into C
In this article, we define the Riemann Integral on functions R into C and proof the linearity of this operator. Especially, the Riemann integral of complex functions is constituted by the redefinition about the Riemann sum of complex numbers. Our method refers to the [19].
Riemann type integrals for functions taking values in a locally convex space
The McShane and Kurzweil-Henstock integrals for functions taking values in a locally convex space are defined and the relations with other integrals are studied. A characterization of locally convex spaces in which Henstock Lemma holds is given.
Riemann-Stieltjes Integral
In this article, the definitions and basic properties of Riemann-Stieltjes integral are formalized in Mizar [1]. In the first section, we showed the preliminary definition. We proved also some properties of finite sequences of real numbers. In Sec. 2, we defined variation. Using the definition, we also defined bounded variation and total variation, and proved theorems about related properties. In Sec. 3, we defined Riemann-Stieltjes integral. Referring to the way of the article [7], we described...
Role of the Harnack extension principle in the Kurzweil-Stieltjes integral
In the theories of integration and of ordinary differential and integral equations, convergence theorems provide one of the most widely used tools. Since the values of the Kurzweil-Stieltjes integrals over various kinds of bounded intervals having the same infimum and supremum need not coincide, the Harnack extension principle in the Kurzweil-Henstock integral, which is a key step to supply convergence theorems, cannot be easily extended to the Kurzweil-type Stieltjes integrals with discontinuous...
Schauder bases in an abstract setting.