A Perron-type integral of order 2 for Riesz spaces

Antonio Boccuto

Mathematica Slovaca (2001)

  • Volume: 51, Issue: 2, page 185-204
  • ISSN: 0139-9918

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Boccuto, Antonio. "A Perron-type integral of order $2$ for Riesz spaces." Mathematica Slovaca 51.2 (2001): 185-204. <http://eudml.org/doc/31720>.

@article{Boccuto2001,
author = {Boccuto, Antonio},
journal = {Mathematica Slovaca},
keywords = {Riesz space; Henstock-Kurzweil integral; Perron integral of order 2; trigonometric series},
language = {eng},
number = {2},
pages = {185-204},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {A Perron-type integral of order $2$ for Riesz spaces},
url = {http://eudml.org/doc/31720},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Boccuto, Antonio
TI - A Perron-type integral of order $2$ for Riesz spaces
JO - Mathematica Slovaca
PY - 2001
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 51
IS - 2
SP - 185
EP - 204
LA - eng
KW - Riesz space; Henstock-Kurzweil integral; Perron integral of order 2; trigonometric series
UR - http://eudml.org/doc/31720
ER -

References

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  1. BOCCUTO A., Differential and integral calculus in Riesz spaces, Tatra Mountains Math. Publ. 14 (1998), 293-323. (1998) MR1651221
  2. BOCCUTO A., Integration by parts with respect to the Henstock-Stieltjes integral in Riesz spaces, Preprint, University of Perugia, 1999. (1999) 
  3. BOCCUTO A., The Perron-Stieltjes integral in Riesz spaces, Preprint, University of Perugia, 1999. (1999) 
  4. BULLEN P. S., A survey of integration by parts for Perron integrals, J. Austral. Math. Soc. Ser. A 40 (1986), 343-363. (1986) Zbl0609.26005MR0832974
  5. BULLEN P. S., The Pn-integral, Bull. Austral. Math. Soc. 14 (1972), 219-236. (1972) MR0320244
  6. DUCHOŇ M.-RIEČAN B., On the Kurzweil-Stieltjes integral in ordered spaces, Tatra Mountains Math. Publ. 8 (1996), 133-142. (1996) Zbl0918.28013MR1475272
  7. JAMES R. D., A generalized integral II, Canad. J. Math. 2 (1950), 297-306. (1950) Zbl0037.17501MR0036344
  8. LUXEMBURG W. A. J.-ZAANEN A. C, Riesz Spaces I, North-Holland Publishing Co., Amsterdam, 1971. (1971) MR0511676
  9. PFEFFER W. F., The Riemann Approach to Integration, Cambridge Univ. Press, Cambridge, 1993. (1993) Zbl0804.26005MR1268404
  10. RIEČAN B., On the Kurzweil integral for functions with values in ordered spaces I, Acta Math. Univ. Comenian. 56-57 (1989), 411-424. (1989) MR1083014
  11. RIEČAN B.-NEUBRUNN T., Integral, Measure and Ordering, Kluwer Acad. Publ.; Ister Science, Dordrecht; Bratislava, 1997. (1997) Zbl0916.28001MR1489521
  12. SKLYARENKO V. A., Some properties of the P2 integral, Mat. Zametki 12 (1972), 693-700 (Russian) [English transl.: Math. USSR Sbornik 12 (1974), 856-860]. (1972) 
  13. ZYGMUND A., Trigonometric Series, Vol. I, Cambridge Univ. Press, Cambridge, 1968. (1968) MR0236587
  14. ZYGMUND A., Trigonometric Series, Vol. II, Cambridge Univ. Press, Cambridge, 1968. (1968) MR0236587

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