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 variation topology
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 Whitney pairs
A simple arc ϕ is said to be a Whitney arc if there exists a non-constant function f such that for every . G. Petruska raised the question whether there exists a simple arc ϕ for which every subarc is a Whitney arc, but for which there is no parametrization satisfying . We answer this question partially, and study the structural properties of possible monotone, strictly monotone and VBG* functions f and associated Whitney arcs.
On Λ-bounded variation
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.
Peano Baker series convergence for matrix-valued functions of bounded variation.
Processus gaussiens à variation finie
Properties of functions of generalized bounded variation
Regulated functions
The first section consists of auxiliary results about nondecreasing real functions. In the second section a new characterization of relatively compact sets of regulated functions in the sup-norm topology is brought, and the third section includes, among others, an analogue of Helly's Choice Theorem in the space of regulated functions.
Regulated functions and the Perron-Stieltjes integral
Regulated functions with values in Banach space
This paper deals with regulated functions having values in a Banach space. In particular, families of equiregulated functions are considered and criteria for relative compactness in the space of regulated functions are given.
Relativization of some aspects of the theory of functions of bounded variation [Book]
Representability of V[h] as intersection of Λ-bounded variation classes
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...
Rotation methods in operator ergodic theory.
-valued maps minimizing the norm of the gradient with free discontinuities
Smooth rough paths and applications to Fourier analysis.