They are using continuous cohomology, so that $$ H^n(G,M) = \varinjlim H^n(G/H,M^H) $$ if $G$ is topological and $M$ is continuous $G$-module (the limit runs over open compact subgroups $H$ of $G$). Look in p. 38 for the definition.

They are using continuous cohomology, so that $$ H^n(G,M) = \varinjlim H^n(G/H,M^H) $$ if $G$ is topological and $M$ is discrete (thanks Arjit) $G$-module (the limit runs over open compact subgroups $H$ of $G$). Look in p. 38 for the definition.