The Banach-Saks property and Haar null sets
Matoušková, Eva
Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998), p. 71-80 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 1998-01-01
Classification:  28A75,  46B20 
@article{118986,
     author = {Eva Matou\v skov\'a},
     title = {The Banach-Saks property and Haar null sets},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {39},
     year = {1998},
     pages = {71-80},
     zbl = {0937.46011},
     mrnumber = {1622974},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118986}
}

Matoušková, Eva. The Banach-Saks property and Haar null sets. Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) pp. 71-80. http://gdmltest.u-ga.fr/item/118986/

Aronszajn N. Differentiability of Lipschitzian mappings between Banach spaces, Studia Math. LVII (1976), 147-190. (1976) | MR 0425608 | Zbl 0342.46034

Baernstein A. On reflexivity and summability, Studia Math. 42 (1972), 91-94. (1972) | MR 0305044 | Zbl 0228.46014

Beauzamy B.; Lapreste J.T. Modèles étalés des espaces de Banach, Travaux en cours, Hermann, Paris, 1984. | MR 0770062 | Zbl 0553.46012

Bessaga C.; Pelczynski A. Selected Topics in Infinite-Dimensional Topology, PWN, Warszawa, 1975. | MR 0478168 | Zbl 0304.57001

Christensen J.P.R. Topology and Borel Structure, North-Holland, Amsterdam, 1974. | MR 0348724 | Zbl 0273.28001

Guerre-Delabrière S. Classical Sequences in Banach Spaces, Marcel Dekker, New York, 1992. | MR 1197117

Hunt B.R. The prevalence of continuous nowhere differentiable functions, Proc. Amer. Math. Soc. 122 (1994), 711-717. (1994) | MR 1260170 | Zbl 0861.26003

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. (1992) | MR 1161274

Lindenstrauss J.; Tzafriri L. Clasical Banach Spaces I., Springer-Verlag, Berlin, 1977. | MR 0500056

Matoušková E. Convexity and Haar null sets, Proc. Amer. Math. Soc. 125 6 (1997), 1793-1799. (1997) | MR 1372040

Matoušková E.; Stegall C. A characterization of reflexive Banach spaces, Proc. Amer. Math. Soc 124 4 (1996), 1083-1090. (1996) | MR 1301517

Mycielski J. Some unsolved problems on the prevalence of ergodicity, instability, and algebraic independence, Ulam Quarterly, vol 1, no. 3 (1992), 30-37. | MR 1208681 | Zbl 0846.28006

Parthasarathy K.R. Probability Measures on Metric Spaces, Academic Press, New York, 1967. | MR 0226684

Solecki S. On Haar null sets, Fundam. Math. 149 (1996), 205-210. (1996) | MR 1383206 | Zbl 0887.28006