Projections of random Cantor sets (Q1823533)

From the closed unit square in the plane closed subsquares are removed by an iterative random process. The remaining points form a fractal which is projected onto the x-axis. The author calculates the almost-sure box- counting dimension of this projection in a rather short way [cf. \textit{F. M. Dekking} and \textit{G. R. Grimmett}, Probab. Theory Relat. Fields 78, 335-355 (1988; Zbl 0628.60091)] and shows that the Hausdorff dimension is almost surely equal to the box-counting dimension. He indicates that there is no difficulty in extending the proof to higher-dimensional cases.