Local dimension for piecewise monotonic maps on the interval

The local dimension of invariant and conformal measures for piecewise monotonic transformations on the interval is considered. For ergodic invariant measures m with positive characteristic exponent chi(m) we show that the local dimension exists almost everywhere and equals h(m)/chi(m). For certain conformal measures we show a relation between a pressure function and the Hausdorff dimension of sets, on which the local dimension is constant.