  Let G be a locally compact topological group and X a compact space with
continuous G-action. The main result of this essay states that the following
statements are equivalent : 1) The action of G on X is topologically amenable ;
2) Every dual (G, X)-module of type C is a relatively injective Banach G-module
; 3) There is a G-invariant element in the double dual of C(X, L1(G)).
