Geodesic
The Range of Invariant Means on Locally Compact Abelian Groups
Canadian mathematical bulletin, Tome 17 (1974) no. 4, pp. 567-573

Voir la notice de l'article provenant de la source Cambridge University Press

It has been shown by E. Granirer that for certain infinite amenable discrete groups G there exists a nested family of left almost convergent subsets of G on which every left invariant mean on m(G) attains as its range the entire [0,1] interval. This paper examines the range of left invariant means on L ∞(G) for infinite locally compact abelian groups G and demonstrates the existence in every such group of a nested family of left almost convergent Borel subsets on which every left invariant mean on L ∞ (G) attains as its range the interval [0,1],
DOI : 10.4153/CMB-1974-101-8
Mots-clés : 43A07, 28A70 
Snell, Roy C. The Range of Invariant Means on Locally Compact Abelian Groups. Canadian mathematical bulletin, Tome 17 (1974) no. 4, pp. 567-573. doi: 10.4153/CMB-1974-101-8
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[1] 1. Granirer, E., On the range of an invariant mean Trans. Amer. Math. Soc. 125 (1966), 384-394. Google Scholar

[2] 2. Hewitt, E. and Ross, K. A., Abstract Harmonic Analysis I, Springer-Verlag (1963). Google Scholar

[3] 3. Reiter, H., Classical Harmonic Analysis and Locally Compact Groups, Oxford Press (1968). Google Scholar

[4] 4. Snell, R., The range of invariant means on locally compact groups and semigroups, Proc. Amer. Math. Soc. 37(1973), 441-447. Google Scholar

[5] 5. Lindenstraus, J., A short proof of Liapounoff's Convexity Theorem, J. of Math, and Mech. 15 (1966), 971-972. Google Scholar

[6] 6. Wong, J., Topologically Stationary Locally Compact Groups and Amenability, Trans. Amer. Math. Soc. 144 (1969) 351-363. Google Scholar

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