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 L p(S;X), which are the vector-valued counterparts of the Lebesgue integral and the classical L p-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.
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© 2016 Springer International Publishing AG
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Hytönen, T., van Neerven, J., Veraar, M., Weis, L. (2016). Bochner spaces. In: Analysis in Banach Spaces . Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, vol 63. Springer, Cham. https://doi.org/10.1007/978-3-319-48520-1_1
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DOI: https://doi.org/10.1007/978-3-319-48520-1_1
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-319-48520-1
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