On the derivative of type α
On the difference property of Borel measurable functions
If an atomlessly measurable cardinal exists, then the class of Lebesgue measurable functions, the class of Borel functions, and the Baire classes of all orders have the difference property. This gives a consistent positive answer to Laczkovich's Problem 2 [Acta Math. Acad. Sci. Hungar. 35 (1980)]. We also give a complete positive answer to Laczkovich's Problem 3 concerning Borel functions with Baire-α differences.
On the differences of upper semicontinuous quasi-continuous functions
On the differentiability of certain saltus functions
We investigate several natural questions on the differentiability of certain strictly increasing singular functions. Furthermore, motivated by the observation that for each famous singular function f investigated in the past, f’(ξ) = 0 if f’(ξ) exists and is finite, we show how, for example, an increasing real function g can be constructed so that for all rational numbers x and g’(x) = 0 for almost all irrational numbers x.
On the differentiability of multivalued mappings. I.
On the differentiability of multivalued mappings. II.
On the Differentiability of the Coordinate Functions of Póyla's Space-Filling Curve.
On the Differentiability Points of a Function of Two Real Variables Admitting Partial Derivatives.
On the differentiation of convex functions
On the differentiation of convex functions in finite and infinite dimensional spaces
On the differentiation of integrals of functions from Lφ(L)
On the differentiation of integrals of functions from Orlicz classes
On the Dirichlet problem for functions of the first Baire class
Let be a simplicial function space on a metric compact space . Then the Choquet boundary of is an -set if and only if given any bounded Baire-one function on there is an -affine bounded Baire-one function on such that on . This theorem yields an answer to a problem of F. Jellett from [8] in the case of a metrizable set .
On the distribution of the number of real zeros of a random polynomial.
On the distribution on the roots of polynomials
Using classical results on conjugate functions, we give very short proofs of theorems of Erdös–Turán and Blatt concerning the angular distribution of the roots of polynomials. Then we study some examples.
On the domain of the implicit function and applications.
On the dominance relation between ordinal sums of conjunctors
This contribution deals with the dominance relation on the class of conjunctors, containing as particular cases the subclasses of quasi-copulas, copulas and t-norms. The main results pertain to the summand-wise nature of the dominance relation, when applied to ordinal sum conjunctors, and to the relationship between the idempotent elements of two conjunctors involved in a dominance relationship. The results are illustrated on some well-known parametric families of t-norms and copulas.
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 Durrmeyer-type modification of some discrete approximation operators.
On the embedding