How do the typical \(L^q\)-dimensions of measures behave? (Q2926585)

For a compact set \(K\subset \mathbb{R}^{d}\) the author computes the value of the upper and of the lower \(L_{q}\)-dimension of a typical probability measure with a support contained in \(K\) for any \(q\in \mathbb{R}\). Different definitions of the ``dimension'' of \(K\) are involved in computing these values, following \(q\in \mathbb{R}\). The paper is very technical and the techniques of the proofs are hard.