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

Toshiharu Kawasaki

Czechoslovak Mathematical Journal (2009)

  • Volume: 59, Issue: 2, page 401-417
  • ISSN: 0011-4642

Abstract

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In a previous paper we defined a Denjoy integral for mappings from a vector lattice to a complete vector lattice. In this paper we define a Henstock-Kurzweil integral for mappings from a vector lattice to a complete vector lattice and consider the relation between these two integrals.

How to cite

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Kawasaki, Toshiharu. "Denjoy integral and Henstock-Kurzweil integral in vector lattices. II." Czechoslovak Mathematical Journal 59.2 (2009): 401-417. <http://eudml.org/doc/37931>.

@article{Kawasaki2009,
abstract = {In a previous paper we defined a Denjoy integral for mappings from a vector lattice to a complete vector lattice. In this paper we define a Henstock-Kurzweil integral for mappings from a vector lattice to a complete vector lattice and consider the relation between these two integrals.},
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 = {401-417},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Denjoy integral and Henstock-Kurzweil integral in vector lattices. II},
url = {http://eudml.org/doc/37931},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Kawasaki, Toshiharu
TI - Denjoy integral and Henstock-Kurzweil integral in vector lattices. II
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 2
SP - 401
EP - 417
AB - In a previous paper we defined a Denjoy integral for mappings from a vector lattice to a complete vector lattice. In this paper we define a Henstock-Kurzweil integral for mappings from a vector lattice to a complete vector lattice and consider the relation between these two integrals.
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/37931
ER -

References

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  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. Kawasaki, T., Denjoy integral and Henstock-Kurzweil integral in vector lattices, I, (to appear). MR2532373
  13. Kubota, Y., Theory of the Integral, Japanese Maki (1977). (1977) 
  14. Lee, P. Y., Lanzhou Lectures on Henstock Integration, World Scientific (1989). (1989) Zbl0699.26004MR1050957
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  17. Riečan, B., Neubrunn, T., Integral, Measure, and Ordering, Kluwer (1997). (1997) MR1489521
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