Abstract
I have already introduced (cf. §§3.1.2 and 3.2.3) the vector space L1(μ;ℝ) with the norm1 ║ . ║L1(μ;ℝ) and shown it to be a Banach space: that is, a normed vector space that is complete with respect to the metric determined by its norm.
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© 2011 Springer Science+Business Media, LLC
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Stroock, D.W. (2011). Basic Inequalities and Lebesgue Spaces. In: Essentials of Integration Theory for Analysis. Graduate Texts in Mathematics, vol 262. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1135-2_6
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DOI: https://doi.org/10.1007/978-1-4614-1135-2_6
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