On closed additive semigroups in $E^{n}$
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- by Christoph Bandelow
- Proc. Amer. Math. Soc. 34 (1972), 87-89
- DOI: https://doi.org/10.1090/S0002-9939-1972-0292993-3
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Abstract:
Let $C(A)$ be the closed additive semigroup generated by a set $A \subset {E^n}$. A simple necessary and sufficient condition on A for $C(A)$ to be a group is derived. An example which arose in the theory of random walks and stimulated these purely geometrical considerations is discussed at the end.References
- C. Bandelow, Recurrence properties of functionals of Markov chains, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 19 (1971), 1–18. MR 315788, DOI 10.1007/BF01111204
- K. L. Chung and W. H. J. Fuchs, On the distribution of values of sums of random variables, Mem. Amer. Math. Soc. 6 (1951), 12. MR 40610
- H. G. Eggleston, Convexity, Cambridge Tracts in Mathematics and Mathematical Physics, No. 47, Cambridge University Press, New York, 1958. MR 0124813
- G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, Oxford, at the Clarendon Press, 1954. 3rd ed. MR 0067125
Bibliographic Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 34 (1972), 87-89
- MSC: Primary 22A15; Secondary 50A05, 60J15
- DOI: https://doi.org/10.1090/S0002-9939-1972-0292993-3
- MathSciNet review: 0292993