Zeros of integrals along trajectories of ergodic non-singular flows (Q1824054)

\textit{D. Ullmann} [Pac. J. Math. 130, No.1, 187-193 (1987; Zbl 0635.28007)] extended a result of Atkinson to non-invariant measures: If \(\tau\) is an ergodic conservative nonsingular transformation, then \[ \liminf | \sum^{n}_{0}(f\circ \tau^ j)(d\mu \circ \tau^ j/d\mu)| =0 \] holds if and only if \(\int f d\mu =0\). The author obtains a continuous time version of this.