In this note, the authors investigate the Hausdorff dimension of the possible time singular set of weak solutions to the Navier-Stokes equation on the three dimensional torus under some regularity conditions of Serrin's type (Arch. Rational Mech. Anal., 9, 187-195, 1962). The results in the paper relate the regularity conditions of Serrin's type to the Hausdorff dimension of the time singular set. More precisely, the authors prove that if a weak solution u belongs to L' (0, T
Va) then the (1 - r(2a-1)/4)-dimensional Hausdorff measure of the time singular set of u is zero. Here, r is just assumed to be positive. the authors also establish that if a weak solution u belongs to L'(0, T
Wl,q) then the (1 - r(2q-3)/2q)-dimensional Hausdorff measure of the time singular set of u is zero. When r = 2, a = 1, or r = 2, q = 2, the authors recover a result of Leray (Acta Math. 63, 193-248, 1934), Scheffer(Commun. Math. Phys. 55, 97-112, 1977), Foias and Temam (1. Math. Pures Appl. 58, 339-368,1979), and Temam (Navier-Stokes equations and nonlinear functional analysis. SIAM, Philadelphia, 1995). the results in some way also relate to the regularity results obtained by Giga (J. Differ. Equ. 62, 186-212, 1986).