Abstract
In this paper, Lebesgue decomposition type theorems for non-additive measure are shown under the conditions of null-additivity, converse null-additivity, weak null-additivity and σ-null-additivity, etc.. In our discussion, the monotone continuity of set function is not required.
This work was partially supported by the NSFC Grant No.70471063, as well as by the Subject Building Foundation of Communication University of China (No. XK060106).
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Li, J., Yasuda, M., Li, J. (2007). A Version of Lebesgue Decomposition Theorem for Non-additive Measure. In: Torra, V., Narukawa, Y., Yoshida, Y. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2007. Lecture Notes in Computer Science(), vol 4617. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73729-2_16
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DOI: https://doi.org/10.1007/978-3-540-73729-2_16
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