A Class of Singular Continuous Functions.
A class of subadditively continuous real functions
A classification of separable Rosenthal compacta and its applications [Book]
A Classification Of Solutions Of Second Order Linear Differential Equations By Means Of Regularly Varying Functions
A companion of Ostrowski's inequality for mappings whose first derivatives are bounded and applications in numerical integration
A comparison of three recent selection theorems
We compare a recent selection theorem given by Chistyakov using the notion of modulus of variation, with a selection theorem of Schrader based on bounded oscillation and with a selection theorem of Di Piazza-Maniscalco based on bounded -oscillation.
A concept of absolute continuity and a Riemann type integral
We present a descriptive definition of a multidimensional generalized Riemann integral based on a concept of generalized absolute continuity for additive functions of sets of bounded variation.
A concise proof for properties of three functions involving the exponential function.
A condition of Busemann-Feller type for the derivation of integrals of functions in the class Φ (L).
A constructive integral equivalent to the integral of Kurzweil
We slightly modify the definition of the Kurzweil integral and prove that it still gives the same integral.
A continous version of Orlicz-Pettis theorem via vector-valued Henstock-Kurzweil integrals
We show that a Pettis integrable function from a closed interval to a Banach space is Henstock-Kurzweil integrable. This result can be considered as a continuous version of the celebrated Orlicz-Pettis theorem concerning series in Banach spaces.
A convergence theory of some methods of integration.
A converse of the Arsenin–Kunugui theorem on Borel sets with σ-compact sections
Let f be a Borel measurable mapping of a Luzin (i.e. absolute Borel metric) space L onto a metric space M such that f(F) is a Borel subset of M if F is closed in L. We show that then is a set for all except countably many y ∈ M, that M is also Luzin, and that the Borel classes of the sets f(F), F closed in L, are bounded by a fixed countable ordinal. This gives a converse of the classical theorem of Arsenin and Kunugui. As a particular case we get Taĭmanov’s theorem saying that the image of...
A converse to some inequalities and approximations in the theory of Stieltjes and stochastic integrals, and for nth derivatives
A counter example on common periodic points of functions.
A counterexample to a Fedorenko statement.
A Daniell integral approach to nonstandard Kurzweil-Henstock integral
A workable nonstandard definition of the Kurzweil-Henstock integral is given via a Daniell integral approach. This allows us to study the HL class of functions from . The theory is recovered together with a few new results.
A dense subsemigroup of S(R) generated by two elements
A derivative to match the v-integral.
A descriptive definition of a BV integral in the real line
A descriptive characterization of a Riemann type integral, defined by BV partition of unity, is given and the result is used to prove a version of the controlled convergence theorem.