Sizes of sets of invariant means

Author(s):  
Alan Paterson
Keyword(s):  
1967 ◽  
Vol 18 (1) ◽  
pp. 120-120 ◽  
Author(s):  
Robert Kaufman
Keyword(s):  

1994 ◽  
Vol 46 (4) ◽  
pp. 808-817
Author(s):  
Tianxuan Miao

AbstractLet with . If G is a nondiscrete locally compact group which is amenable as a discrete group and m ∈ LIM(CB(G)), then we can embed into the set of all extensions of m to left invariant means on L∞(G) which are mutually singular to every element of TLIM(L∞(G)), where LIM(S) and TLIM(S) are the sets of left invariant means and topologically left invariant means on S with S = CB(G) or L∞(G). It follows that the cardinalities of LIM(L∞(G)) ̴ TLIM(L∞(G)) and LIM(L∞(G)) are equal. Note that which contains is a very big set. We also embed into the set of all left invariant means on CB(G) which are mutually singular to every element of TLIM(CB(G)) for G = G1 ⨯ G2, where G1 is nondiscrete, non–compact, σ–compact and amenable as a discrete group and G2 is any amenable locally compact group. The extension of any left invariant mean on UCB(G) to CB(G) is discussed. We also provide an answer to a problem raised by Rosenblatt.


1980 ◽  
Vol 90 (3) ◽  
pp. 233-235 ◽  
Author(s):  
G. A. Margulis
Keyword(s):  

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