The Kurzweil construction of an integral in ordered spaces

Beloslav Riečan; Marta Vrábelová

Czechoslovak Mathematical Journal (1998)

  • Volume: 48, Issue: 3, page 565-574
  • ISSN: 0011-4642

Abstract

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This paper generalizes the results of papers which deal with the Kurzweil-Henstock construction of an integral in ordered spaces. The definition is given and some limit theorems for the integral of ordered group valued functions defined on a Hausdorff compact topological space T with respect to an ordered group valued measure are proved in this paper.

How to cite

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Riečan, Beloslav, and Vrábelová, Marta. "The Kurzweil construction of an integral in ordered spaces." Czechoslovak Mathematical Journal 48.3 (1998): 565-574. <http://eudml.org/doc/30437>.

@article{Riečan1998,
abstract = {This paper generalizes the results of papers which deal with the Kurzweil-Henstock construction of an integral in ordered spaces. The definition is given and some limit theorems for the integral of ordered group valued functions defined on a Hausdorff compact topological space $T$ with respect to an ordered group valued measure are proved in this paper.},
author = {Riečan, Beloslav, Vrábelová, Marta},
journal = {Czechoslovak Mathematical Journal},
keywords = {lattice ordered group valued function and measure; Kurzweil-Henstock construction of an integral; limit theorems; lattice ordered group valued function; lattice ordered group valued measure; Kurzweil-Henstock integral; limit theorems},
language = {eng},
number = {3},
pages = {565-574},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The Kurzweil construction of an integral in ordered spaces},
url = {http://eudml.org/doc/30437},
volume = {48},
year = {1998},
}

TY - JOUR
AU - Riečan, Beloslav
AU - Vrábelová, Marta
TI - The Kurzweil construction of an integral in ordered spaces
JO - Czechoslovak Mathematical Journal
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 48
IS - 3
SP - 565
EP - 574
AB - This paper generalizes the results of papers which deal with the Kurzweil-Henstock construction of an integral in ordered spaces. The definition is given and some limit theorems for the integral of ordered group valued functions defined on a Hausdorff compact topological space $T$ with respect to an ordered group valued measure are proved in this paper.
LA - eng
KW - lattice ordered group valued function and measure; Kurzweil-Henstock construction of an integral; limit theorems; lattice ordered group valued function; lattice ordered group valued measure; Kurzweil-Henstock integral; limit theorems
UR - http://eudml.org/doc/30437
ER -

References

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  1. Riesz spaces, integration and sandwich theorems, Tatra Mountains Math. Publ. 3 (1993), 213–230. (1993) Zbl0815.28007MR1278536
  2. On the Kurzweil-Stieltjes integral in ordered spaces, Tatra Mountains Math. Publ 8 (1996), 133–141. (1996) MR1475272
  3. On integration in complete vector lattices, Tatra Mountains Math. Publ. 3 (1993), 201–212. (1993) MR1278535
  4. The General Theory of Integration, Oxford, 1991. (1991) Zbl0745.26006MR1134656
  5. Nicht absolut konvergente Integrale, Teubner Leipzig, 1980. (1980) MR0597703
  6. On the Kurzweil integral in compact topological spaces, Rad. Mat. 2 (1986), 151–163. (1986) MR0873695
  7. On the Kurzweil integral for functions with values in ordered spaces I, Acta Math. Univ. Comeniana 56–57 (1990), 75–83. (1990) MR1083014
  8. On the Kurzweil integral for functions with values in ordered spaces II, Math. Slov. 43 (1993), 471–475. (1993) MR1248980
  9. On integration with respect to operator valued measures in Riesz spaces, Tatra Mountains Math. Publ. 2 (1993), 149–165. (1993) MR1251049
  10. The fundamental theorem of calculus in an abstract setting, Tatra Mountains Math. Publ. 2 (1993), 167–174. (1993) MR1251050
  11. On the Kurzweil integral for functions with values in ordered spaces III, Tatra Mountains Math. Publ 8 (1996), 93–100. (1996) MR1475267

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