The rangeIα(Lp) of the Riesz potential operator, defined in the sense of distributions in the casep≥n/α, is shown to consist of regular distributions. Moreover, it is shown thatIα(Lp) ⊂Lploc (Rn) for all 1≤p<∞ and 0<α<∞. The distribution space used is that of Lizorkin, which is invariant with respect to the Riesz operator.