Defining Limits by Means of Integrals

Boccuto, Antonio; Candeloro, Domenico

doi:10.1007/978-3-0346-0211-2_7

Antonio Boccuto³⁹ &
Domenico Candeloro³⁹

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 201))

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Abstract

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.

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Authors and Affiliations

Dipartimento di Matematica e Informatica, via Vanvitelli, 1, I-06123, Perugia, Italy
Antonio Boccuto & Domenico Candeloro

Authors

Antonio Boccuto
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Domenico Candeloro
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Editors and Affiliations

Facultad de Matemáticas, Universidad de Sevilla, 41080, Sevilla, Spain
Guillermo P. Curbera
Fachbereich 6: Mathematik, Universität Siegen, 57068, Siegen, Germany
Gerd Mockenhaupt
Mathematisch-Geographische Fakultät, Katholische Universität Eichstätt-Ingolstadt, 85072, Eichstätt, Germany
Werner J. Ricker

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Boccuto, A., Candeloro, D. (2009). Defining Limits by Means of Integrals. In: Curbera, G.P., Mockenhaupt, G., Ricker, W.J. (eds) Vector Measures, Integration and Related Topics. Operator Theory: Advances and Applications, vol 201. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0211-2_7

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DOI: https://doi.org/10.1007/978-3-0346-0211-2_7
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0346-0210-5
Online ISBN: 978-3-0346-0211-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)

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