Singular measures of circle homeomorphisms with two break points

Let $T_f$ be a circle homeomorphism with two break points $a_b,c_b$ and irrational rotation number ${\varrho }_f$. Suppose that the derivative $Df$ of its lift $f$ is absolutely continuous on every connected interval of the set $S^1\mathrm{\backslash }\{a_b,c_b\}$, that $DlogDf\in L^1$ and the product of the jump ratios of $Df$ at the break points is nontrivial, i.e. $\frac{D{f}_{-}(a_b)}{D{f}_{+}(a_b)}\frac{D{f}_{-}(c_b)}{D{f}_{+}(c_b)}\mathrm{\ne }1$. We prove that the unique $T_f$- invariant probability measure ${\mu }_f$ is then singular with respect to Lebesgue measure $l$ on $S^1$.