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Banach Spaces L p

In: Essentials of Measure Theory

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  • Carlos S. Kubrusly

    (Catholic University of Rio de Janeiro, Electrical Engineering Department)

Abstract

A topology to equip the linear space $$\mathcal{L}(X,\mathcal{X},\mu )$$ which will turn it into a Banach space is investigated in this chapter. Section 5.1 summarizes the basics on normed spaces that will be required in Chapter 5 (as well as in parts of Chapters and 6 , 10 , and 12 ). We assume the reader has been introduced to linear spaces (or vector space) before — see e.g., Lemma 4.5.

Suggested Citation

  • Carlos S. Kubrusly, 2015. "Banach Spaces L p," Springer Books, in: Essentials of Measure Theory, edition 1, chapter 5, pages 71-87, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-22506-7_5
    DOI: 10.1007/978-3-319-22506-7_5
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