On the effect of projections on the Billingsley dimensions.

We are interested in the behavior of Billingsley dimensions under projections onto a lower dimensional linear subspace. The results in this paper establish the connections with various dimensions of subsets E of ℝ n and their projections, and generalize many known results about Hausdorff and packing dimensions of projections of E. In particular, we improve, through these results, one of the main theorems of Selmi et al. in [Multifractal variation for projections of measures, Chaos Solitons Fractals  91 (2016) 414–420] and treat an unsolved case in their work. [ABSTRACT FROM AUTHOR]