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<i> S(t)</i> in the interval (t -<i> A,t</i> + A) with<i> А</i> = 4, 39 lnln lnln<i> T</i> for each<i> t, T t T</i> +<i> H</i>, excluding values from the set<i> E</i> with measure mes(E) =<i> O</i> (H(lnln<i>T</i>)<sup>-1</sup>(lnlnln<i>T</i>)<sup>-0,5</sup>) is proved.