Author:
Juan Carlos Ferrando Centro de Investigación Operativa, Edificio Torretamarit, Avda de la Universidad, Universidad Miguel Hernández, E-03202 Elche (Alicante), Spain

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Abstract

Let (Ω,Σ,μ) be a complete finite measure space and X a Banach space. If all X-valued Pettis integrals defined on (Ω,Σ,μ) have separable ranges we show that the space of all weakly μ-measurable (classes of scalarly equivalent) X-valued Pettis integrable functions with integrals of finite variation, equipped with the variation norm, contains a copy of c0 if and only if X does.

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  • [7] Ferrando, J. C. 1994 When does bvca (Σ,X) contain a copy of ? Math. Scand. 74 271274.

  • [8] Ferrando, J. C. 2002 On sums of Pettis integrable random elements Quaestiones Math. 25 311316 .

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  • [13] Musial, K. 2002 Pettis integral Handbook of Measure Theory 531586 .

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  • [16] Talagrand, M. 1984 Quand l'espace des mesures à variation bornée est-il faiblement séquentiellement complet? Proc. Amer. Math. Soc. 90 285288.

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation
1950
Volumes
per Year
3
Issues
per Year
6
Founder Magyar Tudományos Akadémia  
Founder's
Address
H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

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