Density and invariant means in left amenable locally compact topological groups.

Amenable groups have a close relationship with various mathematical concepts. In this paper we consider the correlation between the amenability and semigroup compactification of a locally compact group. It is observed that in the case that G is an amenable group, there are some wonderful properties for G LUC . Motivated by the definition provided by N. Hindman and D. Strauss, we defined the set L I M 0 ( G ) and other sets such as Φ ( G ) and Δ ⁎ ( G ) to achieve the desired results and we considered the correlation between the amenability and semigroup compactification of a locally compact group. [ABSTRACT FROM AUTHOR]