Tafeln der eindeutig umkehrbaren Functionen zweier Variabeln auf den einfachsten Zahlengebieten.
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Schröder (1887)
Mathematische Annalen
Jan Malý (1994)
Commentationes Mathematicae Universitatis Carolinae
Let be a mapping in the Sobolev space . Then the change of variables, or area formula holds for provided removing from counting into the multiplicity function the set where is not approximately Hölder continuous. This exceptional set has Hausdorff dimension zero.
Katuhiko Kanazashi, Hiroyuki Okazaki, Yasunari Shidama (2013)
Formalized Mathematics
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].
A. L. Brown, H. L. Vasudeva (2000)
Winfried Sickel, Leszek Skrzypczak, Jan Vybíral (2014)
Banach Center Publications
We continue our earlier investigations of radial subspaces of Besov and Lizorkin-Triebel spaces on . This time we study characterizations of these subspaces by differences.
Malešević, Branko J., Jovović, Ivana V. (2007)
Journal of Integer Sequences [electronic only]
Miroslav Zelený (2008)
Annales de l’institut Fourier
We construct a differentiable function () such that the set is a nonempty set of Hausdorff dimension . This answers a question posed by Z. Buczolich.
Keiko Narita, Artur Korniłowicz, Yasunari Shidama (2012)
Formalized Mathematics
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.
Libor Veselý (1993)
Commentationes Mathematicae Universitatis Carolinae
For convex continuous functions defined respectively in neighborhoods of points in a normed linear space, a formula for the distance between and in terms of (i.eẇithout using the dual) is proved. Some corollaries, like a new characterization of the subdifferential of a continuous convex function at a point, are given. This, together with a theorem from [4], implies a sufficient condition for a family of continuous convex functions on a barrelled normed linear space to be locally uniformly...
Wolfgang B. Jurkat (1993)
Czechoslovak Mathematical Journal
Wolfgang B. Jurkat, D. J. F. Nonnenmacher (1995)
Czechoslovak Mathematical Journal
Dariusz Idczak (1996)
Banach Center Publications
In the paper, the generalization of the Du Bois-Reymond lemma for functions of two variables to the case of partial derivatives of any order is proved. Some application of this theorem to the coercive Dirichlet problem is given.
Baldomero Rubio (1975)
Collectanea Mathematica
Gonzalez-Velasco, Enrique A. (1987)
International Journal of Mathematics and Mathematical Sciences
Elia, M., Angeli, M.T.Galizia (1984)
Publications de l'Institut Mathématique. Nouvelle Série
Semenov, V. I. (2001)
Sibirskij Matematicheskij Zhurnal
Lothar Berg (1993)
Aequationes mathematicae
Konstancja Bobecka, Jacek Wesołowski (2002)
Studia Mathematica
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...
Piotr Hajłasz, Jacob Mirra (2013)
Analysis and Geometry in Metric Spaces
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.
Luisa Di Piazza, Valeria Marraffa (2002)
Czechoslovak Mathematical Journal
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...
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