The Lebesgue integral as a Riemann integral.
The length of a lemmiscate.
The linear topological quasiconformality coefficient and sufficient conditions for the branch points of mappings.
The local structure of the solutions of the multidimensional translation equation.
The Lukacs-Olkin-Rubin theorem without invariance of the "quotient"
The Lukacs theorem is one of the most brilliant results in the area of characterizations of probability distributions. First, because it gives a deep insight into the nature of independence properties of the gamma distribution; second, because it uses beautiful and non-trivial mathematics. Originally it was proved for probability distributions concentrated on (0,∞). In 1962 Olkin and Rubin extended it to matrix variate distributions. Since that time it has been believed that the fundamental reason...
The Lusin Theorem and Horizontal Graphs in the Heisenberg Group
In this paper we prove that every collection of measurable functions fα , |α| = m, coincides a.e. withmth order derivatives of a function g ∈ Cm−1 whose derivatives of order m − 1 may have any modulus of continuity weaker than that of a Lipschitz function. This is a stronger version of earlier results of Lusin, Moonens-Pfeffer and Francos. As an application we construct surfaces in the Heisenberg group with tangent spaces being horizontal a.e.
The McShane, PU and Henstock integrals of Banach valued functions
Some relationships between the vector valued Henstock and McShane integrals are investigated. An integral for vector valued functions, defined by means of partitions of the unity (the PU-integral) is studied. In particular it is shown that a vector valued function is McShane integrable if and only if it is both Pettis and PU-integrable. Convergence theorems for the Henstock variational and the PU integrals are stated. The families of multipliers for the Henstock and the Henstock variational integrals...
The origin and developments of Kurzweil's generalized Riemann integral
The paper describes to origin and motivation of Kurzweil in introducing a Riemann-type definition for generalized Perron integrals and his further contributions to the topics.
The plenary hull of the generalized Jacobian matrix and the inverse function theorem in subdifferential calculus
The quasi-real extension of the real numbers
The Schur-harmonic-convexity of dual form of the Hamy symmetric function
The singular set of the minima of certain quadratic functionals
The space : minimal connection and optimal lifting
The sum of two plane convex C... sets is not always C...
The use of conjugate convex functions in complex analysis
Traces of Oscillating Functions.
Transformations which preserve convexity.
Two classes of Darboux-like, Baire one functions of two variables
Among the many characterizations of the class of Baire one, Darboux real-valued functions of one real variable, the 1907 characterization of Young and the 1997 characterization of Agronsky, Ceder, and Pearson are particularly intriguing in that they yield interesting classes of functions when interpreted in the two-variable setting. We examine the relationship between these two subclasses of the real-valued Baire one defined on the unit square.
Two new mappings associated with inequalities of Hadamard-type for convex functions.
Two Propositions On Slowly Varying Functions