Abstract
In this section we prove the Ascoli–Arzelà-type compactness theorem introduced in §1.3.2. The theorem is fundamental since a variety of compactness results on various function spaces follows. Here we give a detailed proof, since the case that the domain of definition of functions is not compact is usually not contained in elementary course books.
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© 2010 Springer Science+Business Media, LLC
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Giga, MH., Giga, Y., Saal, J. (2010). Compactness Theorems. In: Nonlinear Partial Differential Equations. Progress in Nonlinear Differential Equations and Their Applications, vol 79. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4651-6_5
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DOI: https://doi.org/10.1007/978-0-8176-4651-6_5
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Publisher Name: Birkhäuser Boston
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Online ISBN: 978-0-8176-4651-6
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