On the Fractal Measures and Dimensions of Image Measures on a Class of Moran Sets

In this work, we focus on the centered Hausdorff measure, packing and Hewitt–Stromberg measure that determines modified lower box dimension Moran fractal sets. The equivalence of these measures for a class is shown by having strong separation condition. We give sufficient condition equality dimension, dimensions. As an application, obtain some relevant conclusions about dimensions image τ-invariant ergodic Borel probability measures. Moreover, statistical interpretation to corresponding geometrical