Riemann type integrals for functions taking values in a locally convex space

Valeria Marraffa

Czechoslovak Mathematical Journal (2006)

  • Volume: 56, Issue: 2, page 475-490
  • ISSN: 0011-4642

Abstract

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The McShane and Kurzweil-Henstock integrals for functions taking values in a locally convex space are defined and the relations with other integrals are studied. A characterization of locally convex spaces in which Henstock Lemma holds is given.

How to cite

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Marraffa, Valeria. "Riemann type integrals for functions taking values in a locally convex space." Czechoslovak Mathematical Journal 56.2 (2006): 475-490. <http://eudml.org/doc/31041>.

@article{Marraffa2006,
abstract = {The McShane and Kurzweil-Henstock integrals for functions taking values in a locally convex space are defined and the relations with other integrals are studied. A characterization of locally convex spaces in which Henstock Lemma holds is given.},
author = {Marraffa, Valeria},
journal = {Czechoslovak Mathematical Journal},
keywords = {Pettis integral; McShane integral; Kurzweil-Henstock integral; locally convex spaces; Pettis integral; McShane integral; Kurzweil-Henstock integral; locally convex spaces},
language = {eng},
number = {2},
pages = {475-490},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Riemann type integrals for functions taking values in a locally convex space},
url = {http://eudml.org/doc/31041},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Marraffa, Valeria
TI - Riemann type integrals for functions taking values in a locally convex space
JO - Czechoslovak Mathematical Journal
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 2
SP - 475
EP - 490
AB - The McShane and Kurzweil-Henstock integrals for functions taking values in a locally convex space are defined and the relations with other integrals are studied. A characterization of locally convex spaces in which Henstock Lemma holds is given.
LA - eng
KW - Pettis integral; McShane integral; Kurzweil-Henstock integral; locally convex spaces; Pettis integral; McShane integral; Kurzweil-Henstock integral; locally convex spaces
UR - http://eudml.org/doc/31041
ER -

References

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  8. The McShane integral in a locally convex space, Rocky Mountain  J. (2006) (to appear). (ARRAY(0x8d70b80)) 
  9. 10.1090/S0002-9947-1969-0239391-0, Trans. Amer. Math. Soc. 137 (1969), 115–123. (1969) MR0239391DOI10.1090/S0002-9947-1969-0239391-0
  10. The Henstock integral for functions with values in nuclear spaces, Math. Japonica 39 (1994), 309–335. (1994) Zbl0927.26011MR1270642
  11. Equivalence of the McShane and Bochner integrals for functions with values in Hilbertian (UCs-N) spaces endowed with nuclearity, Math. Japonica 47 (1998), 261–272. (1998) MR1615121
  12. Nuclear Locally Convex Spaces, Springer-Verlag, Berlin and New York, 1972. (1972) Zbl0308.47024MR0350360
  13. Metric Linear Spaces, D.  Reidel Publishing Company, Warszawa, 1985. (1985) Zbl0573.46001MR0808176
  14. A variational integral for Banach-valued functions, R.A.E. 24 (1998/9), 799–806. (1998/9) MR1704751

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