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

top
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

top

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

top
  1. 10.1007/BF02789840, Analysis Math. 23 (1997), 241–257. (1997) MR1629973DOI10.1007/BF02789840
  2. Integration in locally convex spaces, Simon Stevin 55 (1981), 81–102. (1981) Zbl0473.46031MR0635095
  3. 10.1215/ijm/1258138268, Illinois J.  Math. 45 (2001), 279–289. (2001) MR1849999DOI10.1215/ijm/1258138268
  4. Analyse Fonctionnelle, T. II, Mesure et Intégration dans L’Espace Euclidien  E n , Birkhauser-Verlag, Basel, 1972. (1972) 
  5. 10.1215/ijm/1255986628, Illinois J.  Math. 39 (1995), 39–67. (1995) Zbl0810.28006MR1299648DOI10.1215/ijm/1255986628
  6. 10.1215/ijm/1255986891, Illinois J.  Math. 38 (1994), 127–147. (1994) MR1245838DOI10.1215/ijm/1255986891
  7. 10.1215/ijm/1255988170, Illinois J.  Math. 34 (1990), 557–567. (1990) Zbl0685.28003MR1053562DOI10.1215/ijm/1255988170
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.