Equivalence-singularity dichotomies from zero-one laws
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- by Raoul D. LePage and V. Mandrekar
- Proc. Amer. Math. Soc. 31 (1972), 251-254
- DOI: https://doi.org/10.1090/S0002-9939-1972-0290442-2
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Abstract:
In this note a general result on equivalence and singularity of two measures is presented. As a consequence of this S. Kakutani’s dichotomy for product measures and J. Feldman’s dichotomy for Gaussian measures are derived via appropriate zero-one laws.References
- Jacob Feldman, Equivalence and perpendicularity of Gaussian processes, Pacific J. Math. 8 (1958), 699–708. MR 102760
- Shizuo Kakutani, On equivalence of infinite product measures, Ann. of Math. (2) 49 (1948), 214–224. MR 23331, DOI 10.2307/1969123
- G. Kallianpur, Zero-one laws for Gaussian processes, Trans. Amer. Math. Soc. 149 (1970), 199–211. MR 266293, DOI 10.1090/S0002-9947-1970-0266293-4
- Charles Kraft, Some conditions for consistency and uniform consistency of statistical procedures, Univ. California Publ. Statist. 2 (1955), 125–141. MR 73896
- Michel Loève, Probability theory, 3rd ed., D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1963. MR 0203748
- Jacques Neveu, Bases mathématiques du calcul des probabilités, Masson et Cie, Éditeurs, Paris, 1964 (French). MR 0198504
- Emanuel Parzen, Probability density functionals and reproducing kernel Hilbert spaces. , Proc. Sympos. Time Series Analysis (Brown Univ., 1962) Wiley, New York, 1963, pp. 155–169. MR 0149634
Bibliographic Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 31 (1972), 251-254
- DOI: https://doi.org/10.1090/S0002-9939-1972-0290442-2
- MathSciNet review: 0290442