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Banach Spaces

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Part of the Graduate Texts in Mathematics book series (GTM,volume 282)


We begin this chapter with a quick review of the essentials of metric spaces. Then we extend our results on measurable functions and integration to complex-valued functions. After that, we rapidly review the framework of vector spaces, which allows us to consider natural collections of measurable functions that are closed under addition and scalar multiplication.

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© 2020 Sheldon Axler

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Axler, S. (2020). Banach Spaces. In: Measure, Integration & Real Analysis. Graduate Texts in Mathematics, vol 282. Springer, Cham.

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