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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The nonexistence of ``liftings'' for arithmetic density


Author: H. Weizsäcker
Journal: Proc. Amer. Math. Soc. 86 (1982), 692-693
MSC: Primary 28A51; Secondary 10K99, 10L10
MathSciNet review: 674107
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Abstract: P. Erdös, answering a question of D. Maharam, proved that arithmetic density as a set function does not admit an analogue of measure theoretic liftings [1, Theorem 4]. Here we give a quick proof of this which works in a slightly more general situation.


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DOI: https://doi.org/10.1090/S0002-9939-1982-0674107-7
Keywords: Arithmetic density, lifting, finitely additive measures
Article copyright: © Copyright 1982 American Mathematical Society