An integral defined by approximating $BV$ partitions of unity
Kurzweil, Jaroslav ; Mawhin, Jean ; Pfeffer, Washek Frank
Czechoslovak Mathematical Journal, Tome 41 (1991), p. 695-712 / Harvested from Czech Digital Mathematics Library
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Publié le : 1991-01-01
Classification:  26A45,  26B30 
@article{102500,
     author = {Jaroslav Kurzweil and Jean Mawhin and Washek Frank Pfeffer},
     title = {An integral defined by approximating $BV$ partitions of unity},
     journal = {Czechoslovak Mathematical Journal},
     volume = {41},
     year = {1991},
     pages = {695-712},
     zbl = {0763.26007},
     mrnumber = {1134958},
     language = {en},
     url = {http://dml.mathdoc.fr/item/102500}
}

Kurzweil, Jaroslav; Mawhin, Jean; Pfeffer, Washek Frank. An integral defined by approximating $BV$ partitions of unity. Czechoslovak Mathematical Journal, Tome 41 (1991) pp. 695-712. http://gdmltest.u-ga.fr/item/102500/

A. S. Besicovitch On sufficient conditions for a function to be analytic, and behaviour of analytic functions in the neighbourhood of non-isolated singular points, Proc. London Math. Soc., 32: 1-9, 1931. (1931) | Article

K. J. Falconer The Geometry of Fractal Sets, Cambridge Univ. Press, Cambridge, 1985. (1985) | MR 0867284 | Zbl 0587.28004

H. Federer Geometric Measure Theory, Springer-Verlag, New York, 1969. (1969) | MR 0257325 | Zbl 0176.00801

E. Giusti Minimal Surfaces and Functions of Bounded Variation, Birkhäuser, Basel, 1984. (1984) | MR 0775682 | Zbl 0545.49018

R. Henstock Theory of Integration, Butterworth, London, 1963. (1963) | MR 0158047 | Zbl 0154.05001

E. J. Howard Analyticity of almost everywhere differentiable functions, Proc. American Math. Soc., to appear. | MR 1027093 | Zbl 0705.30001

J. Jarník; J. Kurzweil A nonabsoluteIy convergent integral which admits transformation and can be used for integration on manifolds, Czechoslovak Math. J., 35: 116-139, 1985. (1985) | MR 0779340

J. Jarník; J. Kurzweil A new and more powerful concept of the $PU$-integral, Czechoslovak Math. J., 38: 8-48, 1988. (1988) | MR 0925939

J. Kurzweil Generalized ordinary differential equations and continuous dependence on a parameter, Czechoslovak Math. J., 82: 418-446, 1957. (1957) | MR 0111875 | Zbl 0090.30002

J. Kurzweil; J. Jarník The $PU$-integral: its definition and some basic properties, In New integrals, Lecture Notes in Math. 1419, pages 66-81, Springer-Verlag, New York, 1990. (1990) | MR 1051921

W. F. Pfeffer The Gauss-Green theorem, Advances in Mathematics, to appear. | MR 0995997 | Zbl 1089.26006

W. F. Pfeffer A Riemann type definition of a variational integral, To appear. | MR 1072090 | Zbl 0749.26006

W. F. Pfeffer A Volterra type derivative of the Lebesgue integral, To appear. | MR 1135079 | Zbl 0789.28005

W. F. Pfeffer The multidimensional fundamental theorem of calculus, J. Australian Math. Soc., 43: 143-170, 1987. (1987) | Article | MR 0896622 | Zbl 0638.26011

W. Riidin Real and Complex Analysis, McGraw-Hill, New York, 1987. (1987)

5. Saks Theory of the Integral, Dover, New York, 1964. (1964) | MR 0167578

W. L. C. Sargent On the integrability of a product, J. London Math. Soc., 23: 28-34, 1948. (1948) | Article | MR 0026113 | Zbl 0031.29201

A. I. Volpert The spaces $BV$ and quasilinear equations, Math. USSR-Sbornik, 2: 225-267, 1967. (1967) | Article | MR 0216338

W. P. Ziemer Weakly Differentiable Functions, Springer-Verlag, New York, 1989. (1989) | MR 1014685 | Zbl 0692.46022