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 χ m we show that the local dimension exists almost everywhere and equals h m /χ 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.