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B. Bongiorno, Washek Frank Pfeffer (1992)
Commentationes Mathematicae Universitatis Carolinae
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.
P. Wynn (1976)
Journal für die reine und angewandte Mathematik
Ang, D.D., Schmitt, K., Le, Vy Khoi (1997)
Bulletin of the Belgian Mathematical Society - Simon Stevin
Jiří Jarník, Jaroslav Kurzweil (1984)
Časopis pro pěstování matematiky
Dietmar Treiber (1974)
Mémoires de la Société Mathématique de France
Ruffa, Anthony A. (2004)
International Journal of Mathematics and Mathematical Sciences
Guoju Ye, Peng Yee Lee (2003)
Mathematica Bohemica
We give a Riemann-type definition of the double Denjoy integral of Chelidze and Djvarsheishvili using the new concept of filtering.
Ágnes M. Backhausz, Vilmos Komornik, Tivadar Szilágyi (2009)
Czechoslovak Mathematical Journal
We present a simplified integral of functions of several variables. Although less general than the Riemann integral, most functions of practical interest are still integrable. On the other hand, the basic integral theorems can be obtained more quickly. We also give a characterization of the integrable functions and their primitives.
Maria J. Esteban (1987)
Annales de l'I.H.P. Analyse non linéaire
Takashi Tsuboi (1992)
Annales de l'institut Fourier
We investigate the natural domain of definition of the Godbillon-Vey 2- dimensional cohomology class of the group of diffeomorphisms of the circle. We introduce the notion of area functionals on a space of functions on the circle, we give a sufficiently large space of functions with nontrivial area functional and we give a sufficiently large group of Lipschitz homeomorphisms of the circle where the Godbillon-Vey class is defined.
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