A remark on real coboundary cocycles in 𝐿^{∞}-space

Sato, Ryotaro

doi:10.1090/S0002-9939-02-06756-4

A remark on real coboundary cocycles in $L^{\infty }$-space
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Proc. Amer. Math. Soc. 131 (2003), 231-233 Request permission

Abstract:

Let $T$ be an ergodic automorphism of a probability measure space $(\Omega , {\mathcal A},m)$ and let $f$ be a real-valued measurable function on $\Omega$. We deduce a necessary and sufficient condition for the existence of $L^{\infty }$-solutions of the cohomology equation $f=h\circ T-h$, by using the recent result of Alonso, Hong and Obaya.

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