It is known that if $X$ is a Lebesgue probability space, $T:X\to X$ an ergodic measure preserving automorphism, and $n$ a fixed nonzero integer, then a coboundary for the automorphism $T^n$ is also a coboundary for $T$. In this paper, the result is extended to include the case where the exponent $n=m(x)$ is an arbitrary integrable integer valued function on $X$.
"Coboundaries under Integrable Exponentiation." Tokyo J. Math. 15 (1) 83 - 89, June 1992. https://doi.org/10.3836/tjm/1270130251