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This paper proves some results concerning the lower Hewitt-Stromberg dimension of projections. We give non-trivial lower bounds on the lower Hewitt-Stromberg dimension of the projections onto almost all $m$-dimensional subspaces. In addition, we estimate the dimension of the exceptional sets of $m$-dimensional subspaces where the dimensions of projection are smaller than the typical value. The condition where the quasi-Assouad dimension is no greater than $m$ shows that the lower Hewitt-Stromberg dimension is preserved under orthogonal projections for almost all $m$-dimensional subspaces. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to study average Hewitt-Stromberg and box dimensions of typical compact metric spaces belonging to the Gromov-Hausdorff space equipped with the Gromov-Hausdorff metric. [ABSTRACT FROM AUTHOR]