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

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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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     author = {Snell, Roy C.},
     title = {The {Range} of {Invariant} {Means} on {Locally} {Compact} {Abelian} {Groups}},
     journal = {Canadian mathematical bulletin},
     pages = {567--573},
     year = {1974},
     volume = {17},
     number = {4},
     doi = {10.4153/CMB-1974-101-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1974-101-8/}
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