A strengthening of Leth’s uniqueness condition for sequences

Malitz, Jerome

doi:10.1090/S0002-9939-1986-0861767-4

Proceedings of the American Mathematical Society

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

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A strengthening of Leth’s uniqueness condition for sequences
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by Jerome Malitz PDF

Proc. Amer. Math. Soc. 98 (1986), 641-642 Request permission

Abstract:

A series $\sum {a_i}$ of nonnegative reals summing to 1 such that ${a_i} \leq {\sum _{j > i}}{a_j}$ for eacn $i$ is uniquely characterized by the equalities of the form ${\sum _J}{a_i} = {\sum _K}{a_k}$. This characterization is an improvement of one given by Leth.

References

Rolando Chuaqui and Jerome Malitz, Preorderings compatible with probability measures, Trans. Amer. Math. Soc. 279 (1983), no. 2, 811–824. MR 709585, DOI 10.1090/S0002-9947-1983-0709585-3
Steven Leth, A uniqueness condition for sequences, Proc. Amer. Math. Soc. 93 (1985), no. 2, 287–290. MR 770538, DOI 10.1090/S0002-9939-1985-0770538-8