Monatshefte für Mathematik

, Volume 157, Issue 2, pp 131–142 | Cite as

On Birkhoff integrability for scalar functions and vector measures

  • A. Fernández
  • F. Mayoral
  • F. Naranjo
  • J. Rodríguez
Article
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Abstract

The Bartle–Dunford–Schwartz integral for scalar functions with respect to vector measures is characterized by means of Riemann-type sums based on partitions of the domain into countably many measurable sets. In this setting, two natural notions of integrability (Birkhoff integrability and Kolmogoroff integrability) turn out to be equivalent to Bartle–Dunford–Schwartz integrability.

Keywords

Vector measure Bartle–Dunford–Schwartz integral Birkhoff integral 

Mathematics Subject Classification (2000)

28B05 46G10 
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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • A. Fernández
    • 1
  • F. Mayoral
    • 1
  • F. Naranjo
    • 1
  • J. Rodríguez
    • 2
    • 3
  1. 1.Departamento de Matemática Aplicada II, E.T.S. de IngenierosUniversidad de SevillaSevillaSpain
  2. 2.Departamento de Análisis MatemáticoUniversidad de Valencia, Avda.Burjassot (Valencia)Spain
  3. 3.Instituto Universitario de Matemática Pura y AplicadaUniversidad Politécnica de ValenciaValenciaSpain

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