2023/09/21 by Yao Ouyang, Jun Li, Ouyang, Yao +1
Decision Sciences · #FOS: Mathematics #Functional Analysis (math.FA) #Risk and Portfolio Optimization
paper · pdf · doi:10.48550/arxiv.2309.11868
openalex publication_date 2023/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A version of Radon-Nikodym theorem for the Choquet integral w.r.t. monotone measures is proved. Without any presumptive condition, we obtain a necessary and sufficient condition for the ordered pair (μ, ν) of finite monotone measures to have the so-called Radon-Nikodym property related to a nonnegative measurable function f. If ν is null-continuous and weakly null-additive, then f is uniquely determined almost everywhere by ν and thus is called the Radon-Nikodym derivative of μ w.r.t. ν. For σ-finite monotone measures, a Radon-Nikodym type theorem is also obtained under the assumption that the monotone measures are lower continuous and null-additive.