Denjoy integral and Henstock-Kurzweil integral in vector lattices. I

Toshiharu Kawasaki

Czechoslovak Mathematical Journal (2009)

  • Volume: 59, Issue: 2, page 381-399
  • ISSN: 0011-4642

Abstract

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In this paper we define the derivative and the Denjoy integral of mappings from a vector lattice to a complete vector lattice and show the fundamental theorem of calculus.

How to cite

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Kawasaki, Toshiharu. "Denjoy integral and Henstock-Kurzweil integral in vector lattices. I." Czechoslovak Mathematical Journal 59.2 (2009): 381-399. <http://eudml.org/doc/37930>.

@article{Kawasaki2009,
abstract = {In this paper we define the derivative and the Denjoy integral of mappings from a vector lattice to a complete vector lattice and show the fundamental theorem of calculus.},
author = {Kawasaki, Toshiharu},
journal = {Czechoslovak Mathematical Journal},
keywords = {derivative; Denjoy integral; Henstock-Kurzweil integral; fundamental theorem of calculus; vector lattice; Riesz space; derivative; Denjoy integral; Henstock-Kurzweil integral; fundamental theorem of calculus; vector lattice; Riesz space},
language = {eng},
number = {2},
pages = {381-399},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Denjoy integral and Henstock-Kurzweil integral in vector lattices. I},
url = {http://eudml.org/doc/37930},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Kawasaki, Toshiharu
TI - Denjoy integral and Henstock-Kurzweil integral in vector lattices. I
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 2
SP - 381
EP - 399
AB - In this paper we define the derivative and the Denjoy integral of mappings from a vector lattice to a complete vector lattice and show the fundamental theorem of calculus.
LA - eng
KW - derivative; Denjoy integral; Henstock-Kurzweil integral; fundamental theorem of calculus; vector lattice; Riesz space; derivative; Denjoy integral; Henstock-Kurzweil integral; fundamental theorem of calculus; vector lattice; Riesz space
UR - http://eudml.org/doc/37930
ER -

References

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  2. Boccuto, A., Differential and integral calculus in Riesz spaces, Tatra Mt. Math. Publ. 14 (1998), 293-323. (1998) MR1651221
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  4. Izumi, S., 10.3792/pia/1195573784, Proc. Imp. Acad. Japan 18 (1942), 543-547. (1942) Zbl0061.09909MR0021080DOI10.3792/pia/1195573784
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  6. Kawasaki, T., Order derivative of operators in vector lattices, Math. Japonica 46 (1997), 79-84. (1997) Zbl0907.46038MR1466119
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  9. Kawasaki, T., Approximately order derivatives in vector lattices, Math. Japonica 49 (1999), 229-239. (1999) Zbl0937.47041MR1687642
  10. Kawasaki, T., Order derivative and order Newton integral of operators in vector lattices, Far East J. Math. Sci. 1 (1999), 903-926. (1999) Zbl1069.46507MR1734826
  11. Kawasaki, T., Uniquely determinedness of the approximately order derivative, Sci. Math. Japonicae Online 7 (2002), 333-336 Sci. Math. Japonicae 57 (2003), 365-371. (2003) Zbl1039.46036MR1959995
  12. Kubota, Y., Theory of the Integral, Japanese Maki (1977). (1977) 
  13. Lee, P. Y., Lanzhou Lectures on Henstock Integration, World Scientific (1989). (1989) Zbl0699.26004MR1050957
  14. Luxemburg, W. A. J., Zaanen, A. C., Riesz Spaces, North-Holland (1971). (1971) Zbl0231.46014
  15. McGill, P., 10.1112/jlms/s2-11.3.347, J. London Math. Soc. 11 (1975), 347-360. (1975) Zbl0309.28003MR0393414DOI10.1112/jlms/s2-11.3.347
  16. Riečan, B., Neubrunn, T., Integral, Measure, and Ordering, Kluwer (1997). (1997) MR1489521
  17. Romanovski, P., Intégrale de Denjoy dans les espaces abstraits, Recueil Mathématique (Mat. Sbornik) N. S. 9 (1941), 67-120. (1941) Zbl0026.00302MR0004292
  18. Schaefer, H. H., Banach Lattices and Positive Operators, Springer-Verlag (1974). (1974) Zbl0296.47023MR0423039
  19. Vulikh, B. Z., Introduction to the Theory of Partially Orderd Spaces, Wolters-Noordhoff (1967). (1967) MR0224522

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