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Defining limits by means of integrals. (English) Zbl 1248.28018

Curbera, Guillermo P. (ed.) et al., Vector measures, integration and related topics. Selected papers from the 3rd conference on vector measures and integration, Eichstätt, Germany, September 24–26, 2008. Basel: Birkhäuser (ISBN 978-3-0346-0210-5/hbk; 978-3-0346-0211-2/ebook). Operator Theory: Advances and Applications 201, 79-87 (2010).
Summary: A particular notion of limit is introduced, for Riesz space-valued functions. The definition depends on certain ideals of subsets of the domain. It is shown that, according with our definition, every bounded function with values in a Dedekind complete Riesz space admits limit with respect to any maximal ideal.
For the entire collection see [Zbl 1210.00056].

MSC:

28B15 Set functions, measures and integrals with values in ordered spaces
46G10 Vector-valued measures and integration
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