On Weak Null-Additivity of Monotone Measures

  • Jun Li
  • Radko Mesiar
  • Hemin Wu
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 300)


In this note, the relations between weak null-additivity and pseudometric generating property of monotone measures are discussed. We show that on finite continuous monotone measure spaces \((X, {\cal F}, \mu)\), if measurable space \((X, {\cal F})\) is S-compact (especially, if X is countable), then the weak null-additivity is equivalent to pseudometric generating property. We put a question: abandoning the S-compactness condition, does the equivalence remain valid?


Monotone measure weak null-additivity pseudometric generating property 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jun Li
    • 1
  • Radko Mesiar
    • 2
  • Hemin Wu
    • 3
  1. 1.School of ScienceCommunication University of ChinaBeijingChina
  2. 2.Department of Mathematics and Descriptive Geometry, Faculty of Civil EngineeringSlovak University of TechnologyBratislavaSlovakia
  3. 3.College of Mathematics and Informational TechnologyXinjiang Educational InstituteUrumqiChina

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