Invariant measures on topological groups

In this paper, we prove that every locally KK (see Definition 3.4) topological group has a nonzero outer regular invariant Borel measure when KK is an admissible invariant family which is separated by NGNG. In this case, every open set and every member of S(K0)S(K0) are KK-inner regular. This extends the existence theorem of Haar measure on locally compact Hausdorff groups.