  We investigate Weierstrass functions with roughness parameter $\gamma$ that
are H\"older continuous with coefficient $H={\log\gamma}/{\log \frac12}.$
Analytical access is provided by an embedding into a dynamical system related
to the baker transform where the graphs of the functions are identified as
their global attractors. They possess stable manifolds hosting
Sinai-Bowen-Ruelle (SBR) measures. We systematically exploit a telescoping
property of associated measures to give an alternative proof of the absolute
continuity of the SBR measure for large enough $\gamma$ with square-integrable
density. Telescoping allows a macroscopic argument using the transversality of
the flow related to the mapping describing the stable manifold. The smoothness
of the SBR measure can be used to compute the Hausdorff dimension of the graphs
of the original Weierstrass functions and investigate their local times.
