Change of sign of the function <i>S</i>(<i>t</i>) in short intervals
A theorem for the sign change of the argument of the Riemann zeta function S(t) in the interval (t - A,t + A) with А = 4, 39 lnln lnln T for each t, T t T + H, excluding values from the set E with measure mes(E) = O (H(lnlnT)-1(lnlnlnT)-0,5) is proved.