  For polynomials $f$ on the complex plane with a dendrite Julia set we study
invariant probability measures, obtained from a reference measure. To do this
we follow Keller in constructing canonical Markov extensions. We discuss
``liftability'' of measures (both $f$-invariant and non-invariant) to the
Markov extension, showing that invariant measures are liftable if and only if
they have a positive Lyapunov exponent. We also show that $\delta$-conformal
measure is liftable if and only if the set of points with positive Lyapunov
exponent has positive measure.
