Title:
|
The Banach-Saks property and Haar null sets (English) |
Author:
|
Matoušková, Eva |
Language:
|
English |
Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
ISSN:
|
0010-2628 (print) |
ISSN:
|
1213-7243 (online) |
Volume:
|
39 |
Issue:
|
1 |
Year:
|
1998 |
Pages:
|
71-80 |
. |
Category:
|
math |
. |
Summary:
|
A characterization of Haar null sets in the sense of Christensen is given. Using it, we show that if the dual of a Banach space $X$ has the Banach-Saks property, then closed and convex subsets of $X$ with empty interior are Haar null. (English) |
Keyword:
|
Banach space |
Keyword:
|
convexity |
Keyword:
|
Haar null set |
MSC:
|
28A75 |
MSC:
|
46B20 |
idZBL:
|
Zbl 0937.46011 |
idMR:
|
MR1622974 |
. |
Date available:
|
2009-01-08T18:39:06Z |
Last updated:
|
2012-04-30 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118986 |
. |
Reference:
|
[A] Aronszajn N.: Differentiability of Lipschitzian mappings between Banach spaces.Studia Math. LVII (1976), 147-190. Zbl 0342.46034, MR 0425608 |
Reference:
|
[Ba] Baernstein A.: On reflexivity and summability.Studia Math. 42 (1972), 91-94. Zbl 0228.46014, MR 0305044 |
Reference:
|
[BL] Beauzamy B., Lapreste J.T.: Modèles étalés des espaces de Banach.Travaux en cours, Hermann, Paris, 1984. Zbl 0553.46012, MR 0770062 |
Reference:
|
[BP] Bessaga C., Pelczynski A.: Selected Topics in Infinite-Dimensional Topology.PWN, Warszawa, 1975. Zbl 0304.57001, MR 0478168 |
Reference:
|
[C] Christensen J.P.R.: Topology and Borel Structure.North-Holland, Amsterdam, 1974. Zbl 0273.28001, MR 0348724 |
Reference:
|
[GD] Guerre-Delabrière S.: Classical Sequences in Banach Spaces.Marcel Dekker, New York, 1992. MR 1197117 |
Reference:
|
[H] Hunt B.R.: The prevalence of continuous nowhere differentiable functions.Proc. Amer. Math. Soc. 122 (1994), 711-717. Zbl 0861.26003, MR 1260170 |
Reference:
|
[HSY] Hunt B.R., Sauer T., Yorke J.A.: Prevalence: A translation-invariant ``almost every" on infinite-dimensional spaces.Bull. Amer. Math. Soc. (N.S.) 27 (1992), 217-238. MR 1161274 |
Reference:
|
[LT] Lindenstrauss J., Tzafriri L.: Clasical Banach Spaces I..Springer-Verlag, Berlin, 1977. MR 0500056 |
Reference:
|
[M] Matoušková E.: Convexity and Haar null sets.Proc. Amer. Math. Soc. 125 6 (1997), 1793-1799. MR 1372040 |
Reference:
|
[MS] Matoušková E., Stegall C.: A characterization of reflexive Banach spaces.Proc. Amer. Math. Soc 124 4 (1996), 1083-1090. MR 1301517 |
Reference:
|
[My] Mycielski J.: Some unsolved problems on the prevalence of ergodicity, instability, and algebraic independence.Ulam Quarterly, vol 1, no. 3 (1992), 30-37. Zbl 0846.28006, MR 1208681 |
Reference:
|
[P] Parthasarathy K.R.: Probability Measures on Metric Spaces.Academic Press, New York, 1967. MR 0226684 |
Reference:
|
[S] Solecki S.: On Haar null sets.Fundam. Math. 149 (1996), 205-210. Zbl 0887.28006, MR 1383206 |
. |