A combinatorial analog of Lyapunov's theorem for infinitesimally generated atomic vector measures
Author:
Peter A. Loeb
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
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Abstract | References | Similar Articles | Additional Information
Abstract: It is shown that the range of a measure obtained by the addition of infinitesimal vectors is convex up to infinitesimal errors.
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- [4] 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
- [5] J. F. C. Kingman and A. P. Robertson, On a theorem of Lyapunov, J. London Math. Soc. 43 (1968), 347–351. MR 224768, https://doi.org/10.1112/jlms/s1-43.1.347
- [6] Abraham Robinson, Non-standard analysis, North-Holland Publishing Co., Amsterdam, 1966. MR 0205854
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1973-0316674-3
Keywords:
Reordered series,
partial sums,
Lyapunov theorem,
nonstandard analysis,
infinitesimal atomic vector measures,
convex range
Article copyright:
© Copyright 1973
American Mathematical Society
