The nonexistence of “liftings” for arithmetic density

Weizsäcker, H.

doi:10.1090/S0002-9939-1982-0674107-7

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

The nonexistence of “liftings” for arithmetic density
HTML articles powered by AMS MathViewer

by H. Weizsäcker PDF

Proc. Amer. Math. Soc. 86 (1982), 692-693 Request permission

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.

References

Dorothy Maharam, Finitely additive measures on the integers, Sankhyā Ser. A 38 (1976), no. 1, 44–59. MR 473132