  Following recent result of L. M. T\' oth [arXiv:1906.03137] we show that
every $2\Delta$-regular Borel graph $\mathcal{G}$ with a (not necessarily
invariant) Borel probability measure admits approximate Schreier decoration. In
fact, we show that both ingredients from the analogous statements for finite
graphs have approximate counterparts in the measurable setting, i.e.,
approximate K\H{o}nig's line coloring Theorem for Borel graphs without odd
cycles and approximate balanced orientation for even degree Borel graphs.
