The Banach-Saks property and Haar null sets

Eva Matoušková

Commentationes Mathematicae Universitatis Carolinae (1998)

  • Volume: 39, Issue: 1, page 71-80
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Matoušková, Eva. "The Banach-Saks property and Haar null sets." Commentationes Mathematicae Universitatis Carolinae 39.1 (1998): 71-80. <http://eudml.org/doc/248269>.

@article{Matoušková1998,
abstract = {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.},
author = {Matoušková, Eva},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Banach space; convexity; Haar null set; Banach space; convexity; Haar null set},
language = {eng},
number = {1},
pages = {71-80},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {The Banach-Saks property and Haar null sets},
url = {http://eudml.org/doc/248269},
volume = {39},
year = {1998},
}

TY - JOUR
AU - Matoušková, Eva
TI - The Banach-Saks property and Haar null sets
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1998
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 39
IS - 1
SP - 71
EP - 80
AB - 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.
LA - eng
KW - Banach space; convexity; Haar null set; Banach space; convexity; Haar null set
UR - http://eudml.org/doc/248269
ER -

References

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  9. Lindenstrauss J., Tzafriri L., Clasical Banach Spaces I., Springer-Verlag, Berlin, 1977. MR0500056
  10. Matoušková E., Convexity and Haar null sets, Proc. Amer. Math. Soc. 125 6 (1997), 1793-1799. (1997) MR1372040
  11. Matoušková E., Stegall C., A characterization of reflexive Banach spaces, Proc. Amer. Math. Soc 124 4 (1996), 1083-1090. (1996) MR1301517
  12. Mycielski J., Some unsolved problems on the prevalence of ergodicity, instability, and algebraic independence, Ulam Quarterly, vol 1, no. 3 (1992), 30-37. Zbl0846.28006MR1208681
  13. Parthasarathy K.R., Probability Measures on Metric Spaces, Academic Press, New York, 1967. MR0226684
  14. Solecki S., On Haar null sets, Fundam. Math. 149 (1996), 205-210. (1996) Zbl0887.28006MR1383206

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