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Absolute Continuity of Monotone Measure and Convergence in Measure

  • Conference paper
Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Methods (IPMU 2010)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 80))

Abstract

In this note, the concept of strong absolute continuity of set function is introduced in two different ways. By using the two types of strong absolute continuity of monotone measure, the inheriting of convergence a.e. and convergence in measure for sequence of measurable function under the common addition operation is shown, respectively.

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Author information

Authors and Affiliations

  1. School of Science, Communication University of China, Beijing, 100024, China

    Jun Li

  2. Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, SK-81368, Bratislava, Slovakia

    Radko Mesiar

  3. Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, 30. dubna 22, 701 03, Ostrava 1, Czech Republic

    Radko Mesiar

  4. School of Management and Economics, Beijing Institute of Technology, Beijing, 100081, People’s Republic of China

    Qiang Zhang

Authors
  1. Jun Li
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  2. Radko Mesiar
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  3. Qiang Zhang
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Editor information

Editors and Affiliations

  1. Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Marburg, Germany

    Eyke Hüllermeier

  2. Department of Knowledge Processing and Language Engineering, Otto-von-Guericke University of Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Rudolf Kruse

  3. Fakultät für Elektrotechnik und Informationstechnik, Technische Universität Dortmund, 44221, Dortmund, Germany

    Frank Hoffmann

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Li, J., Mesiar, R., Zhang, Q. (2010). Absolute Continuity of Monotone Measure and Convergence in Measure. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Methods. IPMU 2010. Communications in Computer and Information Science, vol 80. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14055-6_52

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  • DOI: https://doi.org/10.1007/978-3-642-14055-6_52

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14054-9

  • Online ISBN: 978-3-642-14055-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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