Bochner spaces

  • Tuomas Hytönen
  • Jan van Neerven
  • Mark Veraar
  • Lutz Weis
Chapter
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics book series (MATHE3, volume 63)

Abstract

This chapter sets up the general framework in which we work throughout these volumes. After introducing the relevant notions of measurability for functions taking values in a Banach space, we proceed to define the Bochner integral and the Bochner spaces Lp(S;X), which are the vector-valued counterparts of the Lebesgue integral and the classical Lp-spaces, respectively. We also briefly discuss the weaker Pettis integral. The chapter concludes with a detailed investigation of duality of the Bochner spaces and the related Radon–Nikodým property.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Tuomas Hytönen
    • 1
  • Jan van Neerven
    • 2
  • Mark Veraar
    • 3
  • Lutz Weis
    • 4
  1. 1.Department of Mathematics and StatisticsUniversity of HelsinkiHelsinkiFinland
  2. 2.Delft Institute of Applied MathematicsDelft University of TechnologyDelftThe Netherlands
  3. 3.Delft Institute of Applied MathematicsDelft University of TechnologyDelftThe Netherlands
  4. 4.Department of MathematicsKarlsruhe Institute of TechnologyKarlsruheGermany

Personalised recommendations