An answer to a question on the convolution of functions

Let G be a locally compact group. Recently, GaAb and Strobin [2] asked when f*g exists for all , and also: is the set sigma-c-lower porous (in particular, meager) for ? In this paper, we answer these questions. In particular, we prove that if 1 < p < a, 1 a parts per thousand currency sign q < a, and G is a non-unimodular locally compact group, then the set is not lambda -a.e. finite on G} is a residual set in L (p) (G) x L (q) (G).