Gauge integrals and series

Charles W. Swartz

Mathematica Bohemica (2004)

  • Volume: 129, Issue: 3, page 325-332
  • ISSN: 0862-7959

Abstract

top
This note contains a simple example which does clearly indicate the differences in the Henstock-Kurzweil, McShane and strong McShane integrals for Banach space valued functions.

How to cite

top

Swartz, Charles W.. "Gauge integrals and series." Mathematica Bohemica 129.3 (2004): 325-332. <http://eudml.org/doc/249403>.

@article{Swartz2004,
abstract = {This note contains a simple example which does clearly indicate the differences in the Henstock-Kurzweil, McShane and strong McShane integrals for Banach space valued functions.},
author = {Swartz, Charles W.},
journal = {Mathematica Bohemica},
keywords = {Henstock-Kurzweil integral; McShane integral; Henstock-Kurzweil integral; McShane integral},
language = {eng},
number = {3},
pages = {325-332},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Gauge integrals and series},
url = {http://eudml.org/doc/249403},
volume = {129},
year = {2004},
}

TY - JOUR
AU - Swartz, Charles W.
TI - Gauge integrals and series
JO - Mathematica Bohemica
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 129
IS - 3
SP - 325
EP - 332
AB - This note contains a simple example which does clearly indicate the differences in the Henstock-Kurzweil, McShane and strong McShane integrals for Banach space valued functions.
LA - eng
KW - Henstock-Kurzweil integral; McShane integral; Henstock-Kurzweil integral; McShane integral
UR - http://eudml.org/doc/249403
ER -

References

top
  1. Normed Linear Spaces, Springer, New York, 1962. (1962) Zbl0100.10802
  2. 10.1215/ijm/1255986726, Illinois J. Math. 38 (1994), 471–479. (1994) Zbl0797.28006MR1269699DOI10.1215/ijm/1255986726
  3. 10.1215/ijm/1255986891, Illinois J. Math. 38 (1994), 127–147. (1994) MR1245838DOI10.1215/ijm/1255986891
  4. The Integrals of Lebesgue, Denjoy, Perron and Henstock, Amer. Math. Soc., Providence, 1991. (1991) MR1288751
  5. 10.1215/ijm/1255988170, Illinois J. Math. 34 (1990), 557–567. (1990) Zbl0685.28003MR1053562DOI10.1215/ijm/1255988170
  6. Functional Analysis and Semigroups, Amer. Math. Soc., Providence, 1957. (1957) MR0089373
  7. The Integral: an Easy Approach after Kurzweil and Henstock, Cambridge Univ. Press, Cambridge, 2000. (2000) MR1756319
  8. Unified Integration, Academic Press, New York, 1983. (1983) Zbl0551.28001MR0740710
  9. The Riemann Approach to Integration, Cambridge Univ. Press, Cambridge, 1993. (1993) Zbl0804.26005MR1268404
  10. Abstract Bochner and McShane integrals, Ann. Math. Silesianae 10 (1996), 21–56. (1996) Zbl0868.28005MR1399609
  11. 10.1023/A:1013721114330, Czechoslovak Math. J. 51 (2001), 819–828. (2001) MR1864044DOI10.1023/A:1013721114330
  12. 10.36045/bbms/1105737762, Bull. Belgian Math. Soc. 4 (1997), 589–599. (1997) Zbl1038.46505MR1600292DOI10.36045/bbms/1105737762
  13. Infinite Matrices and the Gliding Hump, World Sci. Publ., Singapore, 1996. (1996) Zbl0923.46003MR1423136
  14. Introduction to Gauge Integrals, World Scientific Publ., Singapore, 2001. (2001) Zbl0982.26006MR1845270
  15. A Riemann-type definition of the Bochner integral, J. Math. Study 27 (1994), 32–36. (1994) MR1318255

NotesEmbed ?

top

You must be logged in to post comments.