| Title:
|
An integral defined by approximating $BV$ partitions of unity (English) |
| Author:
|
Kurzweil, Jaroslav |
| Author:
|
Mawhin, Jean |
| Author:
|
Pfeffer, Washek Frank |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
41 |
| Issue:
|
4 |
| Year:
|
1991 |
| Pages:
|
695-712 |
| . |
| Category:
|
math |
| . |
| MSC:
|
26A45 |
| MSC:
|
26B30 |
| idZBL:
|
Zbl 0763.26007 |
| idMR:
|
MR1134958 |
| DOI:
|
10.21136/CMJ.1991.102500 |
| . |
| Date available:
|
2008-06-09T15:42:31Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/102500 |
| . |
| Reference:
|
[1] 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. 10.1112/plms/s2-32.1.1 |
| Reference:
|
[2] K. J. Falconer: The Geometry of Fractal Sets.Cambridge Univ. Press, Cambridge, 1985. Zbl 0587.28004, MR 0867284 |
| Reference:
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[3] H. Federer: Geometric Measure Theory.Springer-Verlag, New York, 1969. Zbl 0176.00801, MR 0257325 |
| Reference:
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[4] E. Giusti: Minimal Surfaces and Functions of Bounded Variation.Birkhäuser, Basel, 1984. Zbl 0545.49018, MR 0775682 |
| Reference:
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[5] R. Henstock: Theory of Integration.Butterworth, London, 1963. Zbl 0154.05001, MR 0158047 |
| Reference:
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[6] E. J. Howard: Analyticity of almost everywhere differentiable functions.Proc. American Math. Soc., to appear. Zbl 0705.30001, MR 1027093 |
| Reference:
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[7] 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. MR 0779340 |
| Reference:
|
[8] J. Jarník, J. Kurzweil: A new and more powerful concept of the $PU$-integral.Czechoslovak Math. J., 38: 8-48, 1988. MR 0925939 |
| Reference:
|
[9] J. Kurzweil: Generalized ordinary differential equations and continuous dependence on a parameter.Czechoslovak Math. J., 82: 418-446, 1957. Zbl 0090.30002, MR 0111875 |
| Reference:
|
[10] 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. MR 1051921 |
| Reference:
|
[11] W. F. Pfeffer: The Gauss-Green theorem.Advances in Mathematics, to appear. Zbl 1089.26006, MR 0995997 |
| Reference:
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[12] W. F. Pfeffer: A Riemann type definition of a variational integral.To appear. Zbl 0749.26006, MR 1072090 |
| Reference:
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[13] W. F. Pfeffer: A Volterra type derivative of the Lebesgue integral.To appear. Zbl 0789.28005, MR 1135079 |
| Reference:
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[14] W. F. Pfeffer: The multidimensional fundamental theorem of calculus.J. Australian Math. Soc., 43: 143-170, 1987. Zbl 0638.26011, MR 0896622, 10.1017/S1446788700029293 |
| Reference:
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[15] W. Riidin: Real and Complex Analysis.McGraw-Hill, New York, 1987. |
| Reference:
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[16] 5. Saks: Theory of the Integral.Dover, New York, 1964. MR 0167578 |
| Reference:
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[17] W. L. C. Sargent: On the integrability of a product.J. London Math. Soc., 23: 28-34, 1948. Zbl 0031.29201, MR 0026113, 10.1112/jlms/s1-23.1.28 |
| Reference:
|
[18] A. I. Volpert: The spaces $BV$ and quasilinear equations.Math. USSR-Sbornik, 2: 225-267, 1967. MR 0216338, 10.1070/SM1967v002n02ABEH002340 |
| Reference:
|
[19] W. P. Ziemer: Weakly Differentiable Functions.Springer-Verlag, New York, 1989. Zbl 0692.46022, MR 1014685 |
| . |
