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
DOI:
https://doi.org/10.1090/S0002-9947-1976-0436244-3
MathSciNet review:
0436244
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We provide a general setting for studying admissible and singular translates of measures on linear spaces. We apply our results to measures on . 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.
- [1] R. M. Dudley, Singular translates of measures on linear spaces, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 3 (1964), 128-137. MR 29 #6529. MR 0169277 (29:6529)
- [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)
- [3] J. Hoffmann-Jørgensen and G. Pisier, The law of large numbers and the central limit theorem in Banach spaces (preprint).
- [4] 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)
- [5] J. D. Kuelbs, Gaussian measures on a Banach space, J. Functional Analysis 5 (1970), 354-367. MR 41 #4639. MR 0260010 (41:4639)
- [6] 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)
- [7] A. Pietsch, Absolut p-summierende Abbildungen in normierten Räumen, Studia Math. 28 (1966/67), 333-353. MR 35 #7162. MR 0216328 (35:7162)
- [8] A. P. Robertson and W. Robertson, Topological vector spaces, Cambridge Univ. Press, New York, 1973. MR 0350361 (50:2854)
- [9] V. N. Sudakov, On the characterization of quasi-invariance of measures in Hilbert space, Uspehi Mat. Nauk 18 (1963), no. 1 (109), 188-190. (Russian) MR 26 #6740. MR 0149250 (26:6740)
- [10] 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)
- [11] J. Zinn, Admissible translates of stable measures, Studia Math. 54 (1975), 245-257. MR 0400376 (53:4210)
Retrieve articles in Transactions of the American Mathematical Society with MSC: 60B05, 28A40, 60G30
Retrieve articles in all journals with MSC: 60B05, 28A40, 60G30
Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1976-0436244-3
Keywords:
Admissible translates,
singular translates,
Skorokhod topology on ,
measures on vector spaces,
quasi-invariant sets
Article copyright:
© Copyright 1976
American Mathematical Society