Abstract: The s-sets have been studied in this paper.Using the Vitali Covering Theorem the author gets a basic property describing the Hausdorff measure of the s-set by the notation of Hs-a.e.closed set covering.As applications,the author obtains the characteristic on the Hausdorff measure of the s-straight s-set.

Key words: s-set, s-straight s-set, Hs-a.e.closed set covering, Hausdorff measure, upper convex density