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A Radon-Nikodym derivative for almost subadditive set functions

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  • Yann Rébillé

    (LEMNA - Laboratoire d'économie et de management de Nantes Atlantique - IEMN-IAE Nantes - Institut d'Économie et de Management de Nantes - Institut d'Administration des Entreprises - Nantes - UN - Université de Nantes)

Abstract

In classical measure theory, the Radon-Nikodym theorem states in a concise condition, namely domination, how a measure can be factorized by another (bounded) measure through a density function. Several approaches have been undertaken to see under which conditions an exact factorization can be obtained with set functions that are not σ-additive (for instance finitely additive set functions or submeasures). We provide a Radon-Nikodym type theorem with respect to a measure for almost subadditive set functions of bounded sum. The necessary and sufficient condition to guarantee a one-sided Radon-Nikodym derivative remains the standard domination condition for measures.

Suggested Citation

  • Yann Rébillé, 2009. "A Radon-Nikodym derivative for almost subadditive set functions," Working Papers hal-00441923, HAL.
    • Handle: RePEc:hal:wpaper:hal-00441923
    Note: View the original document on HAL open archive server: https://hal.science/hal-00441923
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