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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.

 

A combinatorial analog of Lyapunov’s theorem for infinitesimally generated atomic vector measures
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by Peter A. Loeb PDF
Proc. Amer. Math. Soc. 39 (1973), 585-586 Request permission

Abstract:

It is shown that the range of a measure obtained by the addition of infinitesimal vectors is convex up to infinitesimal errors.
References
    V. Bergström, Ein neuer Beweis eines Satzes von E. Steinitz, Abh. Math. Sem. Univ. Hamburg. 8 (1931), 148-154. —, Zwei Sätze über ebene Vectorpolygone, Abh. Math. Sem. Univ. Hamburg. 8 (1931), 206-214. D. J. Brown, Existence of a competitive equilibrium in a nonstandard exchange economy, Cowles Foundation Discussion Paper No. 342, Cowles Foundation for Research in Economics, Yale University, New Haven, Conn.
  • Ira Damsteeg and Israel Halperin, The Steinitz-Gross theorem on sums of vectors, Trans. Roy. Soc. Canada Sect. III 44 (1950), 31–35. MR 38559
  • J. F. C. Kingman and A. P. Robertson, On a theorem of Lyapunov, J. London Math. Soc. 43 (1968), 347–351. MR 224768, DOI 10.1112/jlms/s1-43.1.347
  • Abraham Robinson, Non-standard analysis, North-Holland Publishing Co., Amsterdam, 1966. MR 0205854
  • E. Steinitz, Bedingt konvergente Reihen und konvexe Systeme, J. Reine Angew. Math. 143 (1913), 128-175.
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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 39 (1973), 585-586
  • MSC: Primary 28A45; Secondary 26A98
  • DOI: https://doi.org/10.1090/S0002-9939-1973-0316674-3
  • MathSciNet review: 0316674