ON DENSENESS OF C-0(infinity)(Omega) AND COMPACTNESS IN Lp(x)(Omega) FOR 0 < p(x) < 1

The main goal of this paper is to prove the denseness of C-0(infinity)(Omega) in L-p(x) (Omega)for 0 < p(x) < 1. We construct a family of potential type identity approximations and prove a modular inequality in L-p(x) (Omega)for 0 < p(x) < 1. As an application we prove an analogue of the Kolmogorov Riesz type compactness theorem in L-p(x)(Omega) for 0 < p(x) < 1.