On the Additive Property of Finitely Additive Measures

Ryoichi Kunisada ()
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Ryoichi Kunisada: Waseda University

Journal of Theoretical Probability, 2022, vol. 35, issue 3, 1782-1794

Abstract: 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.

Keywords: Charge; Finitely additive measure; Asymptotic density; Density measure; Primary 28E10; Secondary 28C15 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10959-021-01115-3

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