On subspaces of the spaces L-loc(p) and of their strong duals

For Omega an open subset of IRN and 1 < p < infinity, we prove that any com plemented subspace E of L-loc(p) (Omega) contains either a complemented cop y of (l(2))(IN) or a complemented rely of (l(p))(IN), provided E similar or equal to F, not similar or equal to omega and not similar or equal to omeg a+F with F Banach space. We also prove that any complemented subspace E of (L-loc(p) (Omega))(beta)' contains either a complemented copy of (l(2))((IN )) or a complemented copy of (l(p))((IN)), provided E not similar or equal to F, not similar or equal to phi and not similar or equal to phi + F with F Banach space.