An integral defined by approximating B V partitions of unity

Jaroslav Kurzweil; Jean Mawhin; Washek Frank Pfeffer

Czechoslovak Mathematical Journal (1991)

  • Volume: 41, Issue: 4, page 695-712
  • ISSN: 0011-4642

How to cite

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Kurzweil, Jaroslav, Mawhin, Jean, and Pfeffer, Washek Frank. "An integral defined by approximating $BV$ partitions of unity." Czechoslovak Mathematical Journal 41.4 (1991): 695-712. <http://eudml.org/doc/13963>.

@article{Kurzweil1991,
author = {Kurzweil, Jaroslav, Mawhin, Jean, Pfeffer, Washek Frank},
journal = {Czechoslovak Mathematical Journal},
keywords = { integral; sets; divergence theorem; Kurzweil-Henstock integral; partitions of unity},
language = {eng},
number = {4},
pages = {695-712},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {An integral defined by approximating $BV$ partitions of unity},
url = {http://eudml.org/doc/13963},
volume = {41},
year = {1991},
}

TY - JOUR
AU - Kurzweil, Jaroslav
AU - Mawhin, Jean
AU - Pfeffer, Washek Frank
TI - An integral defined by approximating $BV$ partitions of unity
JO - Czechoslovak Mathematical Journal
PY - 1991
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 41
IS - 4
SP - 695
EP - 712
LA - eng
KW - integral; sets; divergence theorem; Kurzweil-Henstock integral; partitions of unity
UR - http://eudml.org/doc/13963
ER -

References

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  6. E. J. Howard, Analyticity of almost everywhere differentiable functions, Proc. American Math. Soc., to appear. Zbl0705.30001MR1027093
  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. (1985) MR0779340
  8. J. Jarník, J. Kurzweil, A new and more powerful concept of the P U -integral, Czechoslovak Math. J., 38: 8-48, 1988. (1988) MR0925939
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  10. J. Kurzweil, J. Jarník, The P U -integral: its definition and some basic properties, In New integrals, Lecture Notes in Math. 1419, pages 66-81, Springer-Verlag, New York, 1990. (1990) MR1051921
  11. W. F. Pfeffer, The Gauss-Green theorem, Advances in Mathematics, to appear. Zbl1089.26006MR0995997
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  13. W. F. Pfeffer, A Volterra type derivative of the Lebesgue integral, To appear. Zbl0789.28005MR1135079
  14. W. F. Pfeffer, 10.1017/S1446788700029293, J. Australian Math. Soc., 43: 143-170, 1987. (1987) Zbl0638.26011MR0896622DOI10.1017/S1446788700029293
  15. W. Riidin, Real and Complex Analysis, McGraw-Hill, New York, 1987. (1987) 
  16. 5. Saks, Theory of the Integral, Dover, New York, 1964. (1964) MR0167578
  17. W. L. C. Sargent, 10.1112/jlms/s1-23.1.28, J. London Math. Soc., 23: 28-34, 1948. (1948) Zbl0031.29201MR0026113DOI10.1112/jlms/s1-23.1.28
  18. A. I. Volpert, 10.1070/SM1967v002n02ABEH002340, Math. USSR-Sbornik, 2: 225-267, 1967. (1967) MR0216338DOI10.1070/SM1967v002n02ABEH002340
  19. W. P. Ziemer, Weakly Differentiable Functions, Springer-Verlag, New York, 1989. (1989) Zbl0692.46022MR1014685

Citations in EuDML Documents

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  1. Luisa Di Piazza, Valeria Marraffa, The McShane, PU and Henstock integrals of Banach valued functions
  2. Diana Caponetti, Valeria Marraffa, A descriptive definition of a BV integral in the real line
  3. Rudolf Výborný, Kurzweil’s PU integral as the Lebesgue integral
  4. Giuseppa Riccobono, A PU-integral on an abstract metric space
  5. Jiří Jarník, Štefan Schwabik, Jaroslav Kurzweil septuagenarian
  6. Jiří Jarník, Štefan Schwabik, Milan Tvrdý, Ivo Vrkoč, Eighty years of Jaroslav Kurzweil

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