Size of subsets of groups and haar null SETS

Geometric and Functional Analysis

Volumn 15, Issue 1, 2005, Pages 246-273

  Solecki, S ^a  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21944438118     PISSN: 1016443X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00039-005-0505-z     Document Type: Article

References (25)

1. [BK] H. BECKER, A.S. KECHRIS, The Descriptive Set Theory of Polish Group Actions, London Mathematical Society Lecture Notes Series 232, Cambridge University Press, 1996.
2. [BeL] Y. BENYAMINI, J. LINDENSTRAUSS, Geometric Nonlinear Functional Analysis, Colloquium Publications, American Mathematical Society, 2000.
3. [Bi] P. BILLINGSLEY, Probability and Measure, Wiley, 1995.
4. [Cl] J.P.R. CHRISTENSEN, On sets of Haar measure zero in Abelian Polish groups, Israel J. Math. 13 (1972), 255-260.
5. [C2] J.P.R. CHRISTENSEN, Topology and Borel Structure, North-Holland, 1974.
6. [D1] M.M. DAY, Amenable semigroups, Illinois J. Math. 1 (1957), 509-544.
7. [D2] M.M. DAY, Lumpy subsets in left-amenable, locally compact semigroups, Pacific J. Math. 62 (1976), 87-92.
8. [D3] M.M. DAY, Left thick to left lumpy - a guided tour, Pacific. J. Math. 101 (1982), 71-92.
9. [E] W.R. EMERSON, Characterizations of amenable groups, Trans. Amer. Math. Soc. 241 (1978), 183-194.
10. [Er] J. ERDÖS, The theory of groups with finite classes of conjugate elements, Acta Math. Acad. Sci. Hung. 5 (1954), 45-58.
11. [HR] E. HEWITT, K.A. Ross, Abstract Harmonic Analysis, Vol. I, Springer Verlag, 1963.
12. [HSY] B.R. HUNT, T. SAUR, J.A. YORKE, Prevalence: a translation invariant "almost every" on infinite dimensional spaces, Bull. Amer. Math. Soc. (N.S.) 27 (1992), 217-238.
13. [KR] R.V. KADISON, J.R. RINGROSE, Fundamentals of the Theory of Operator Algebras, Vol. II, Academic Press, 1986.
14. [LMP] J. LINDENSTRAUSS, E. MATOUŠKOVA, D. PREISS, Lipschitz image of a measure-null set can have a null complement, Israel J. Math. 118 (2000), 207-219.
15. [LP] J. LINDENSTRAUSS, D. PREISS, On Frechet differentiability of Lipschitz maps between Danach spaces, Ann. of Math. 157 (2003), 257-288.
16. [M] E. MATOUŠKOVA, Translating finite sets into convex sets, Bull. London Math. Soc. 33 (2001), 711-714.
17. [Mi] T. MlTCHELL, Constant functions and left invariant means on semigroups, Trans. Amer. Math. Soc. 119 (1965), 244-261.
18. [My] J. MYCIELSKI, Some unsolved problems on the prevalence of ergodicity, instability, and algebraic independence, Ulam Quarterly 1 (1992), 30-37.
19. [NI] B.H. NEUMANN, Groups with finite conjugacy classes, Proc. London Math. Soc. 1 (1951), 178-187.
20. [N2] B.H. NEUMANN, Groups covered by finitely many cosets, Publ. Math. Debrecen 3 (1954), 227-242.
21. [PI] A.L.T. PATERSON, Amenable groups for which every topological left invariant mean is invariant, Pacific J. Math. 84 (1979), 391-397.
22. [P2] A.L.T. PATERSON, Amenablity, Mathematical Surveys and Monographs 29, Amer. Math. Soc., 1988.
23. [Pi] J.-P. PIER, Amenable Locally Compact Groups, Wiley, 1984.
24. [ST] H. SHI, B.S. THOMSON, Haar null sets in the space of automorphisms of [0,1], Real Anal. Exchange 24 (1998/99), 337-350.
25. [TH] F. TOPSØE, J. HUFFMAN-JØRGENSEN, Analytic spaces and their applications, in "Analytic Sets" (C.A. Rogers et. al., eds.) Academic Press (1980), 317-401.