Abstract
A statement such as “f belongs to an Lp space” can be understood in different ways. The strict interpretation is that f is an equivalence class of functions, the equivalence relation being equality almost everywhere. But one can also think of some representative of this equivalence class, perhaps defined at all points outside a set of measure zero. In particular, if a continuous function is identified with an element in Lp, the identification means that one representative of the corresponding equivalence class is singled out, and this distinguished element is usually thought of as belonging to Lp.
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© 1996 Springer-Verlag Berlin Heidelberg
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Adams, D.R., Hedberg, L.I. (1996). Continuity Properties. In: Function Spaces and Potential Theory. Grundlehren der mathematischen Wissenschaften, vol 314. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03282-4_6
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DOI: https://doi.org/10.1007/978-3-662-03282-4_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08172-9
Online ISBN: 978-3-662-03282-4
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