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Erschienen in:
Classes of Modulars Kapitel lesen Erstes Kapitel lesen

2015 | OriginalPaper | Buchkapitel

5. Bounded and Regulated Mappings

verfasst von : Vyacheslav V. Chistyakov

Erschienen in: Metric Modular Spaces

Verlag: Springer International Publishing

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Abstract

In this chapter, we introduce and study a special \(\mathbb{N}\)-valued modular on the set of all mappings from an interval of the real line into a metric space. We show that the sets of all bounded mappings and regulated mappings (i.e., those, whose one-sided limits exist at each point of the interval) are modular spaces for this modular. We apply the modular to establish a pointwise selection principle, extending the classical Helly Selection Theorem.

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Vorheriges Kapitel Topologies on Modular Spaces
Nächstes Kapitel Mappings of Bounded Generalized Variation
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Metadaten
Titel
Bounded and Regulated Mappings
verfasst von
Vyacheslav V. Chistyakov
Copyright-Jahr
2015
Buch
Metric Modular Spaces

Print ISBN: 978-3-319-25281-0

Electronic ISBN: 978-3-319-25283-4

Copyright-Jahr: 2015

DOI
https://doi.org/10.1007/978-3-319-25283-4_5