Correction to: “Zero-one laws for stable measures” [Proc. Amer. Math. Soc. 45 (1974), 245–252; MR 51 #6901]
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- by R. M. Dudley and Marek Kanter PDF
- Proc. Amer. Math. Soc. 88 (1983), 689-690 Request permission
Abstract:
A law on a vector space (e.g. the plane) with all one-dimensional marginals stable (of index less than 1) need not be stable, by examples of David Marcus. An error in the authors’ proof to the contrary is noted.References
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S. Banach, Théorie des opérations linéaires, 2nd ed., Chelsea, New York, 1963.
- Jens Peter Reus Christensen, Borel structures in groups and semigroups, Math. Scand. 28 (1971), 124–128. MR 308322, DOI 10.7146/math.scand.a-11010
- R. M. Dudley and Marek Kanter, Zero-one laws for stable measures, Proc. Amer. Math. Soc. 45 (1974), 245–252. MR 370675, DOI 10.1090/S0002-9939-1974-0370675-9
- Evarist Giné and Marjorie G. Hahn, On stability of probability laws with univariate stable marginals, Z. Wahrsch. Verw. Gebiete 64 (1983), no. 2, 157–165. MR 714141, DOI 10.1007/BF01844604 G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, 4th ed., Clarendon Press, Oxford, 1960. David J. Marcus, Non-stable laws with all projections stable, Z. Wahrsch. Verw. Gebiete (to appear).
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 88 (1983), 689-690
- MSC: Primary 60B11; Secondary 60E07, 60F20
- DOI: https://doi.org/10.1090/S0002-9939-1983-0702300-4
- MathSciNet review: 702300