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Invariant Means on Locally Compact
Diverse Applications of Invariant
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8-large relative action of G amenable group AP(G Banach space C P(G CB(S closed convex hull compact set compact set K C G convergent to left convex hull convex set convex sums cosets cosets of H define discrete groups Dixmier 11 Ea:ample existence f 6 CB(G finite fixed point property free group func g 6 G G is amenable G-invariant group G Haar measure hence Hulanicki invariant measure left Haar measure left invariant means left translates Lemma Let G LIM on B(G LIM on L°°(G linear functional locally compact group mean on B(G means on L°°(G modular function non-negative proof property P1 prove relatively compact right cosets right invariant mean semi-simple semigroup semigroup of operators strongly convergent subset Theorem tion Tm(s topological group topological left invariance topological LIM trivial two-sided invariant UCB(G unique variant means WAP semigroup weak containment weak containment property weak topology weakly compact