On Tarski's contribution to the additive measure theory and its consequences

doi:10.1016/j.apal.2003.11.004

Annals of Pure and Applied Logic

Volume 126, Issues 1–3, April 2004, Pages 281-286

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Abstract

We recall one Tarski's result about the existence of a non-zero additive measure defined on power set of an infinite set vanishing on finite subsets. This rather surprising result goes back to 1930 and it allows to introduce a non-trivial linear functional invariant under changes of finitely many inputs.

MSC

28A12

Keywords

Additive measure

Choquet integral

Linear functional

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¹: The first version of this paper was written before the unexpected death of Professor Pietro Benvenuti.