Exact dimensionality of Mandelbrot cascades acting on ergodic measures and dimension of projections

In this talk we will show that the push-forward measures of Mandelbrot cascades acting on ergodic measures on symbolic spaces mapped through canonical mapping of one-dimensional iterated functions systems are exact-dimensional. We shall also extend this result to skew product symbolic spaces and apply this to obtain an extension of Hochman and Shmerkin’s projection theorem on product of time 2 and time 3 invariant measures.