Sur les différentielles des fonctions de plusieurs variables indépendantes
Sur les différentielles des fonctions de plusieurs variables indépendantes
Sur les notions de limite et de continuité et sur quelques propriétés générales des fonctions continues d'un nombre quelconque de variables
Sur un problème concernant les fonctions quasicontinues
Sur un théorème relatif à la continuité des fonctions
The C k Space
In this article, we formalize continuous differentiability of realvalued functions on n-dimensional real normed linear spaces. Next, we give a definition of the Ck space according to [23].
The Denjoy-Clarkson property with respect to Hausdorff measures for the gradient mapping of functions of several variables
We construct a differentiable function () such that the set is a nonempty set of Hausdorff dimension . This answers a question posed by Z. Buczolich.
The Differentiable Functions from R into R n
In control engineering, differentiable partial functions from R into Rn play a very important role. In this article, we formalized basic properties of such functions.
The hardy-littlewood maximal function and derivation of integrals.
The local structure of the solutions of the multidimensional translation equation.
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 quasi-real extension of the real numbers
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.
Über den Zwischenwertsatz von Darboux und den Umkehrsatz für differenzierbare Funktion mehrerer Veränderlicher.
Über einen Satz von Khintchine. II.
Ueber die Vollwerthigkeit und die Stetigkeit analytischer Ausdrücke
Uniform limits of Darboux functions on the Euclidean plane
Variations of additive functions
We study the relationship between derivates and variational measures of additive functions defined on families of figures or bounded sets of finite perimeter. Our results, valid in all dimensions, include a generalization of Ward’s theorem, a necessary and sufficient condition for derivability, and full descriptive definitions of certain conditionally convergent integrals.
Whitney arcs and 1-critical arcs
A simple arc γ ⊂ ℝⁿ is called a Whitney arc if there exists a non-constant real function f on γ such that for every x ∈ γ; γ is 1-critical if there exists an f ∈ C¹(ℝⁿ) such that f’(x) = 0 for every x ∈ γ and f is not constant on γ. We show that the two notions are equivalent if γ is a quasiarc, but for general simple arcs the Whitney property is weaker. Our example also gives an arc γ in ℝ² each of whose subarcs is a monotone Whitney arc, but which is not a strictly monotone Whitney arc. This...
Zur Theorie der Functionaldeterminanten. Von Carl Neumann in Leipzig