Recurrence of integral zeros for ergodic flows

Let a flow $T_t$ preserve an ergodic probability measure $\mu$, $\int fd\mu =0$, and $\mu (A)>0$. Then for almost all $x\in A$, for which $f(x)\mathrm{\ne }0$, there is a sequence $t_k\to \mathrm{\infty }$ such that $T_{t_k}x\in A$ and ${\int }_0^{t_k}f(T_{s}x)ds=0$.