TY - JOUR
T1 - Packing dimensions of projections and dimension profiles
AU - Falconer, Kenneth John
AU - Howroyd, JD
N1 - Howroyd was a research assistant of Falconer at the time of writing.
PY - 1997/3
Y1 - 1997/3
N2 - For E a subset of R(n) and 0 less than or equal to m less than or equal to n we define a 'family of dimensions' Dim(m)E, closely related to the packing dimension off, with the property that the orthogonal projection of E onto almost all m-dimensional subspaces has packing dimension Dim(m)E. In particular the packing dimension of almost all such projections must be equal. We obtain similar results for the packing dimension of the projections of measures. We are led to think of Dim(m)E for m is an element of [0, n] as a 'dimension profile' that reflects a variety of geometrical properties of E, and we characterize the dimension profiles that are obtainable in this way.
AB - For E a subset of R(n) and 0 less than or equal to m less than or equal to n we define a 'family of dimensions' Dim(m)E, closely related to the packing dimension off, with the property that the orthogonal projection of E onto almost all m-dimensional subspaces has packing dimension Dim(m)E. In particular the packing dimension of almost all such projections must be equal. We obtain similar results for the packing dimension of the projections of measures. We are led to think of Dim(m)E for m is an element of [0, n] as a 'dimension profile' that reflects a variety of geometrical properties of E, and we characterize the dimension profiles that are obtainable in this way.
KW - SETS
UR - http://www.scopus.com/inward/record.url?scp=21444454260&partnerID=8YFLogxK
M3 - Article
SN - 0305-0041
VL - 121
SP - 269
EP - 286
JO - Mathematical Proceedings of the Cambridge Philosophical Society
JF - Mathematical Proceedings of the Cambridge Philosophical Society
ER -