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On the Additive Property of Finitely Additive Measures

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  • Ryoichi Kunisada

    (Waseda University)

Abstract

By additive property, we refer to a condition under which $$L^p$$ L p spaces over finitely additive measures are complete. In their 2000 paper, Basile and Rao gave a necessary and sufficient condition that a finite sum of finitely additive measures has the additive property. We generalize this result to the case of a countable sum of finitely additive measures. We also apply this result to density measures, the finitely additive probabilities on $$\mathbb {N}$$ N which extend asymptotic density (also called natural density), and provide the necessary and sufficient condition that a certain type of density measure has the additive property.

Suggested Citation

  • Ryoichi Kunisada, 2022. "On the Additive Property of Finitely Additive Measures," Journal of Theoretical Probability, Springer, vol. 35(3), pages 1782-1794, September.
    • Handle: RePEc:spr:jotpro:v:35:y:2022:i:3:d:10.1007_s10959-021-01115-3
    DOI: 10.1007/s10959-021-01115-3
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    References listed on IDEAS

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    1. Michael Spece & Joseph B. Kadane, 2020. "Prime Residue Class of Uniform Charges on the Integers," Journal of Theoretical Probability, Springer, vol. 33(1), pages 340-360, March.
    2. Lauwers, Luc, 1998. "Intertemporal objective functions: Strong pareto versus anonymity," Mathematical Social Sciences, Elsevier, vol. 35(1), pages 37-55, January.
    3. Oliver Schirokauer & Joseph B. Kadane, 2007. "Uniform Distributions on the Natural Numbers," Journal of Theoretical Probability, Springer, vol. 20(3), pages 429-441, September.
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