Let K be a compact set of R n and t ≥ 0. In this paper, we discuss the relation between the t-dimensional Hewitt-Stromberg premeasure and measure denoted by H t and H t respectively. We prove : if H t (K) < +∞ then H t (K) = H t (K) and if H t (K) = +∞, there exists a compact subset F of K such that H t (F) = H t (F) and H t (F) is close as we like to H t (K).