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Banach space; convexity; Haar null set
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.
[A] Aronszajn N.: Differentiability of Lipschitzian mappings between Banach spaces. Studia Math. LVII (1976), 147-190. MR 0425608 | Zbl 0342.46034
[Ba] Baernstein A.: On reflexivity and summability. Studia Math. 42 (1972), 91-94. MR 0305044 | Zbl 0228.46014
[BL] Beauzamy B., Lapreste J.T.: Modèles étalés des espaces de Banach. Travaux en cours, Hermann, Paris, 1984. MR 0770062 | Zbl 0553.46012
[BP] Bessaga C., Pelczynski A.: Selected Topics in Infinite-Dimensional Topology. PWN, Warszawa, 1975. MR 0478168 | Zbl 0304.57001
[C] Christensen J.P.R.: Topology and Borel Structure. North-Holland, Amsterdam, 1974. MR 0348724 | Zbl 0273.28001
[GD] Guerre-Delabrière S.: Classical Sequences in Banach Spaces. Marcel Dekker, New York, 1992. MR 1197117
[H] Hunt B.R.: The prevalence of continuous nowhere differentiable functions. Proc. Amer. Math. Soc. 122 (1994), 711-717. MR 1260170 | Zbl 0861.26003
[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
[LT] Lindenstrauss J., Tzafriri L.: Clasical Banach Spaces I. Springer-Verlag, Berlin, 1977. MR 0500056
[M] Matoušková E.: Convexity and Haar null sets. Proc. Amer. Math. Soc. 125 6 (1997), 1793-1799. MR 1372040
[MS] Matoušková E., Stegall C.: A characterization of reflexive Banach spaces. Proc. Amer. Math. Soc 124 4 (1996), 1083-1090. MR 1301517
[My] 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
[P] Parthasarathy K.R.: Probability Measures on Metric Spaces. Academic Press, New York, 1967. MR 0226684
[S] Solecki S.: On Haar null sets. Fundam. Math. 149 (1996), 205-210. MR 1383206 | Zbl 0887.28006
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