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References
Adyan, S.I.: Random walks on free periodic groups. Math. USSR Izv.21, 425–434 (1983)
Banach, S.: Sur le problème de la mesure. Fundam. Math.4, 7–33 (1923)
Dunwoody, M.J.: Cutting up graphs. Combinatorica2, 15–23 (1982)
Eymard, P.: Moyennes invariantes et représentations unitaires (Lecture Notes Mathematics, Vol. 300). Berlin Heidelberg New York: Springer 1972
Freudenthal, H.: Über die Enden diskreter Räume und Gruppen. Comment. Math. Helv.17, 1–38 (1944)
Grigrochuk, R.I.: Degrees of growth of finitely generated groups, and the theory of invariant means. Math. USSR Izv25, 259–300 (1985)
Halin, R.: Über unendliche Wege in Graphen. Math. Ann.157, 125–137 (1964)
Halin, R.: Die Maximalzahl zweiseitig unendlicher Wege in Graphen. Math. Nachr.44, 119–127 (1970)
Halin, R.: Automorphisms and endomorphisms of infinite locally finite graphs. Abh. Math. Sem. Univ. Hamb.39, 251–283 (1973)
De la Harpe, P., Skandalis, G.: Un résultat de Tarski sur les actions moyennables de groupes et les partitions paradoxales. Enseign. Math., II Sér.32, 121–138 (1986)
Jung, H.A.: Connectivity in infinite graphs. In: Studies in Pure Math., pp. 137–143. L. Mirsky (ed). New York London: Academic Press 1971
Jung, H.A.: A note on fragments of infinite graphs. Combinatorica1, 285–288 (1981)
Ore, O.: Theory of graphs. Providence: Amer. Math. Soc. 1962
Nebbia, C.: On the amenability and the Kunze-Stein property for groups acting on a tree. Pac. J. Math. (to appear)
Picardello, M.A., Woess, W.: Harmonic functions and ends of graphs. Proc. Edin. Math. Soc.31, 457–461 (1988)
Pier, J.P.: Amenable locally compact groups. New York: Wiley 1984
Soardi, P.M., Woess, W.: Amenability, unimodularity, and the spectral radius of random walks on infinite graphs. Preprint, Univ. Milano 1988
Soardi, P.M., Woess, W.: Uniqueness of currents in infinite resistive networks. Discrete Appl. Math. (to appear)
Stallings, J.: Group theory and three-dimensional manifolds. New Haven: Yale Univ. Press 1971
Tits, J.: Sur le groupe des automorphismes d'un arbre. In: Essays on topology and related topics, mémoires dédiés a G. de Rham, pp. 188–211. Berlin Heidelberg New York: Springer 1970
Tits, J.: A “theorem of Lie-Kolchin” for trees. In: Contributions to algebra, a collection of papers dedicated to Ellis Kolchin, pp. 377–388. New York London: Academic Press 1977
Trofimov, V.I.: Automorphism groups of graphs as topological objects. Math. Notes38, 717–720 (1985)
Von Neumann, J.: Zur allgemeinen Theorie des Maßes. Fund. Math.13, 73–116 (1929)
Wagon, S.: The Banach-Tarski paradox. Encyclopedia of Math.24. Cambridge: Cambridge Univ. Press 1985
Woess, W.: Graphs and groups with tree-like properties. J. Combin. Th., Ser. B (to appear)
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Dedicated to Professor Gert Sabidussi on the occasion of his sixtieth birthday
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Woess, W. Amenable group actions on infinite graphs. Math. Ann. 284, 251–265 (1989). https://doi.org/10.1007/BF01442875
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DOI: https://doi.org/10.1007/BF01442875