For a locally compact group G, we prove that a topological inner invariant mean on LUC(G) has an extension to a topological inner invariant mean on L∞(G). Mathematics Subject Classification: 43A07, 43A10

lorentz characterized the almost convergence through the concept of uniform convergence of de lavallée-poussin mean. in this paper, we generalize the notion of almost convergence by using the concept ofinvariant mean and the generalized de la vallée-poussin mean. we determine the bounded linear operators forthe generalized σ-conservative, σ-regular and σ-coercive matrices.