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Admissible and singular translates of measures on vector spaces
Authors:
Alan Gleit and Joel Zinn
Journal:
Trans. Amer. Math. Soc. 221 (1976), 199-211
MSC:
Primary 60B05; Secondary 28A40, 60G30
MathSciNet review:
0436244
Full-text PDF Free Access
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Abstract: We provide a general setting for studying admissible and singular translates of measures on linear spaces. We apply our results to measures on ![$ D[0,1]$](images/img2.gif) . Further, we show that in many cases convex, balanced, bounded, and complete subsets of the admissible translates are compact. In addition, we generalize Sudakov's theorem on the characterization of certain quasi-invariant sets to separable reflexive spaces which have the Central Limit Property.
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- [2]
- R. M. Fortet and E. Mourier, Les fonctions aléatoires comme éléments aléatoires dans les espaces de Banach, Studia Math. 15 (1955), 62-79. MR 19, 1202. MR 0093052 (19:1202b)
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- J. L. Kelley and I. Namioka, Linear topological spaces, University Ser.in Higher Math., Van Nostrand, Princeton, N. J., 1963. MR 29 #3851. MR 0166578 (29:3851)
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- J. D. Kuelbs, Gaussian measures on a Banach space, J. Functional Analysis 5 (1970), 354-367. MR 41 #4639. MR 0260010 (41:4639)
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- J. Lindenstrauss and L. Tzafriri, Classical Banach spaces, Lecture Notes in Math., vol. 338, Springer-Verlag, Berlin and New York, 1973. MR 0415253 (54:3344)
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- A. Pietsch, Absolut p-summierende Abbildungen in normierten Räumen, Studia Math. 28 (1966/67), 333-353. MR 35 #7162. MR 0216328 (35:7162)
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- A. P. Robertson and W. Robertson, Topological vector spaces, Cambridge Univ. Press, New York, 1973. MR 0350361 (50:2854)
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- Dao-Xing Xia (Hsia Tao-hsing), Measure and integration theory on infinite-dimensional spaces. Abstract harmonic analysis, Pure and Appl. Math., vol. 48, Academic Press, New York, 1972. MR 46 #9281. MR 0310179 (46:9281)
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- J. Zinn, Admissible translates of stable measures, Studia Math. 54 (1975), 245-257. MR 0400376 (53:4210)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9947-1976-0436244-3
PII:
S 0002-9947(1976)0436244-3
Keywords:
Admissible translates,
singular translates,
Skorokhod topology on ![$ D[0,1]$](images/img1.gif) ,
measures on vector spaces,
quasi-invariant sets
Article copyright:
© Copyright 1976 American Mathematical Society
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