Riemann type integrals for functions taking values in a locally convex space
Czechoslovak Mathematical Journal, Tome 56 (2006) no. 2, pp. 475-490
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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.
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.
Classification : 26A42, 26E20, 28B05, 46G10
Keywords: Pettis integral; McShane integral; Kurzweil-Henstock integral; locally convex spaces
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Marraffa, V. Riemann type integrals for functions taking values in a locally convex space. Czechoslovak Mathematical Journal, Tome 56 (2006) no. 2, pp. 475-490. http://geodesic.mathdoc.fr/item/CMJ_2006_56_2_a13/

[1] Sk.  Jaker Ali, N. D.  Chakraborty: Pettis integration in locally convex spaces. Analysis Math. 23 (1997), 241–257. | DOI | MR

[2] C.  Blondia: Integration in locally convex spaces. Simon Stevin 55 (1981), 81–102. | MR | Zbl

[3] L.  Di Piazza, K. Musiał: A characterization of variationally McShane integrable Banach-space valued functions. Illinois J.  Math. 45 (2001), 279–289. | DOI | MR

[4] H. G.  Garnir, M.  De Wilde, and J.  Schmets: Analyse Fonctionnelle, T. II, Mesure et Intégration dans L’Espace Euclidien  $E_n$. Birkhauser-Verlag, Basel, 1972.

[5] D. H.  Fremlin: The generalized McShane integral. Illinois J.  Math. 39 (1995), 39–67. | DOI | MR | Zbl

[6] D. H.  Fremlin, J.  Mendoza: On the integration of vector-valued functions. Illinois J.  Math. 38 (1994), 127–147. | DOI | MR

[7] R. A.  Gordon: The McShane integral of Banach-valued functions. Illinois J.  Math. 34 (1990), 557–567. | DOI | MR | Zbl

[8] V.  Marraffa: The McShane integral in a locally convex space. Rocky Mountain  J. (2006) (to appear).

[9] C. W.  McArthur, J. R.  Retherford: Some applications of an inequality in locally convex spaces. Trans. Amer. Math. Soc. 137 (1969), 115–123. | DOI | MR

[10] S.  Nakanishi: The Henstock integral for functions with values in nuclear spaces. Math. Japonica 39 (1994), 309–335. | MR | Zbl

[11] K.  Sakurada, S.  Nakanishi: 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. | MR

[12] A.  Pietsch: Nuclear Locally Convex Spaces. Springer-Verlag, Berlin and New York, 1972. | MR | Zbl

[13] S.  Rolewicz: Metric Linear Spaces. D.  Reidel Publishing Company, Warszawa, 1985. | MR | Zbl

[14] V. A.  Skvortsov, A. P.  Solodov: A variational integral for Banach-valued functions. R.A.E. 24 (1998/9), 799–806. | MR