Let { \mathbb{ V} = V x R^l : V \in G(n-l,m-l)} be the family of m-dimensional subspaces of R^n containing { 0} x R^l, and let \pi_{ \mathbb{ V}} : R^n --> \mathbb{ V} be the orthogonal projection onto \mathbb{ V}. We prove that the mapping V \mapsto Dim \pi_{ \mathbb{ V}}(B) is almost surely constant for any analytic set B \subset R^n, where Dim denotes either Hausdorff or packing dimension.
Categories: math.CA