Full proof of Kwapień's theorem on representing bounded mean zero functions on $[0,1]$

Aleksei F. Ber, Matthijs J. Borst, Fedor A. Sukochev

In [7], Kwapień announced that every mean zero function $f\in L_{\infty }[0,1]$ can be written as a coboundary $f=g\circ T-g$ for some $g\in L_{\infty }[0,1]$ and some measure preserv…