A note on the interior and dimensions of typical sumsets.

Let \mathcal {K} be the collection of all non-empty compact subsets of the unit cube [0,1]^d. Fixing any F_\sigma set F\subset [0,1]^d of Lebesgue measure zero and 0<c<1, we show that for typical K\in \mathcal {K} with \mathcal {L}^d(K)\geq c (in the sense of Baire category), the sumset K+F has empty interior. We also find the Hausdorff, lower and upper box and packing dimensions of K+F for typical K\in \mathcal {K}. [ABSTRACT FROM AUTHOR]